Design and Analysis of Shortened Bose-Chaudhuri-Hocquenghem Codes for Efficient Data Transmission over the Eisenstein Fields Article Swipe

PDF

Muhammad Sajjad , Rafiq Asghar , Mushtaq K. Abdalrahem , Adnan Burhan Rajab , M. Narayana , Moin-ud-Din Junjua , Salman A. AlQahtani ·

YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.29020/nybg.ejpam.v18i3.6275

This article focuses on the constructing and decoding for Shortened Bose-Chaudhuri-Hocquenghem (BCH) codes over the Eisenstein fields, based on the Berlekamp-Massey Algorithm (BMA) with improved decoding performance. Thus, Eisenstein fields, being a natural generalization of Gaussian fields, form a well-devised algebraic structure for error-correcting codes and have better parameters for transmission of information in noisy channels. The work starts with the definition of shortened BCH codes over the Eisenstein fields with the mention of generator polynomials and the study of certain algebraic characteristics. These codes are designed to provide the best balance between the words length and the ability to cope with error detection and correction in variety of high-efficiency applications. The modified BMA is presented as a decoding mechanism that is equipped for the translation of Eisenstein field arithmetic which is different in nature. The modification concerns an improved approach to the residual terms defined by the classes of higher level, which leads to the efficiency of convergence and the reduction of numerical complexity in contrast to the BMA. The imitations show that the proposed codes offer a higher error correcting capability and faster computation compared to the traditional BCH codes over finite fields when reliability and low latency are desired.

Related Topics

Concepts

Mathematics Transmission (telecommunications) Arithmetic Computer science Telecommunications

Metadata

Type: article
Language: en
Landing Page: https://doi.org/10.29020/nybg.ejpam.v18i3.6275
PDF: https://www.ejpam.com/index.php/ejpam/article/download/6275/2221
OA Status: diamond
Related Works: 10
OpenAlex ID: https://openalex.org/W4412825100

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W4412825100

Canonical identifier for this work in OpenAlex
DOI: https://doi.org/10.29020/nybg.ejpam.v18i3.6275

Digital Object Identifier
Title: Design and Analysis of Shortened Bose-Chaudhuri-Hocquenghem Codes for Efficient Data Transmission over the Eisenstein Fields

Work title
Type: article

OpenAlex work type
Language: en

Primary language
Publication year: 2025

Year of publication
Publication date: 2025-08-01

Full publication date if available
Authors: Muhammad Sajjad, Rafiq Asghar, Mushtaq K. Abdalrahem, Adnan Burhan Rajab, M. Narayana, Moin-ud-Din Junjua, Salman A. AlQahtani

List of authors in order
Landing page: https://doi.org/10.29020/nybg.ejpam.v18i3.6275

Publisher landing page
PDF URL: https://www.ejpam.com/index.php/ejpam/article/download/6275/2221

Direct link to full text PDF
Open access: Yes

Whether a free full text is available
OA status: diamond

Open access status per OpenAlex
OA URL: https://www.ejpam.com/index.php/ejpam/article/download/6275/2221

Direct OA link when available
Concepts: Mathematics, Transmission (telecommunications), Arithmetic, Computer science, Telecommunications

Top concepts (fields/topics) attached by OpenAlex
Cited by: 0

Total citation count in OpenAlex
Related works (count): 10

Other works algorithmically related by OpenAlex

Full payload

id	https://openalex.org/W4412825100
doi	https://doi.org/10.29020/nybg.ejpam.v18i3.6275
ids.doi	https://doi.org/10.29020/nybg.ejpam.v18i3.6275
ids.openalex	https://openalex.org/W4412825100
fwci	0.0
type	article
title	Design and Analysis of Shortened Bose-Chaudhuri-Hocquenghem Codes for Efficient Data Transmission over the Eisenstein Fields
biblio.issue	3
biblio.volume	18
biblio.last_page	6275
biblio.first_page	6275
topics[0].id	https://openalex.org/T11130
topics[0].field.id	https://openalex.org/fields/17
topics[0].field.display_name	Computer Science
topics[0].score	0.9977999925613403
topics[0].domain.id	https://openalex.org/domains/3
topics[0].domain.display_name	Physical Sciences
topics[0].subfield.id	https://openalex.org/subfields/1702
topics[0].subfield.display_name	Artificial Intelligence
topics[0].display_name	Coding theory and cryptography
topics[1].id	https://openalex.org/T11321
topics[1].field.id	https://openalex.org/fields/17
topics[1].field.display_name	Computer Science
topics[1].score	0.9930999875068665
topics[1].domain.id	https://openalex.org/domains/3
topics[1].domain.display_name	Physical Sciences
topics[1].subfield.id	https://openalex.org/subfields/1705
topics[1].subfield.display_name	Computer Networks and Communications
topics[1].display_name	Error Correcting Code Techniques
topics[2].id	https://openalex.org/T11797
topics[2].field.id	https://openalex.org/fields/22
topics[2].field.display_name	Engineering
topics[2].score	0.9907000064849854
topics[2].domain.id	https://openalex.org/domains/3
topics[2].domain.display_name	Physical Sciences
topics[2].subfield.id	https://openalex.org/subfields/2208
topics[2].subfield.display_name	Electrical and Electronic Engineering
topics[2].display_name	graph theory and CDMA systems
is_xpac	False
apc_list
apc_paid
concepts[0].id	https://openalex.org/C33923547
concepts[0].level	0
concepts[0].score	0.8264121413230896
concepts[0].wikidata	https://www.wikidata.org/wiki/Q395
concepts[0].display_name	Mathematics
concepts[1].id	https://openalex.org/C761482
concepts[1].level	2
concepts[1].score	0.4244205951690674
concepts[1].wikidata	https://www.wikidata.org/wiki/Q118093
concepts[1].display_name	Transmission (telecommunications)
concepts[2].id	https://openalex.org/C94375191
concepts[2].level	1
concepts[2].score	0.3598576486110687
concepts[2].wikidata	https://www.wikidata.org/wiki/Q11205
concepts[2].display_name	Arithmetic
concepts[3].id	https://openalex.org/C41008148
concepts[3].level	0
concepts[3].score	0.09012335538864136
concepts[3].wikidata	https://www.wikidata.org/wiki/Q21198
concepts[3].display_name	Computer science
concepts[4].id	https://openalex.org/C76155785
concepts[4].level	1
concepts[4].score	0.08673381805419922
concepts[4].wikidata	https://www.wikidata.org/wiki/Q418
concepts[4].display_name	Telecommunications
keywords[0].id	https://openalex.org/keywords/mathematics
keywords[0].score	0.8264121413230896
keywords[0].display_name	Mathematics
keywords[1].id	https://openalex.org/keywords/transmission
keywords[1].score	0.4244205951690674
keywords[1].display_name	Transmission (telecommunications)
keywords[2].id	https://openalex.org/keywords/arithmetic
keywords[2].score	0.3598576486110687
keywords[2].display_name	Arithmetic
keywords[3].id	https://openalex.org/keywords/computer-science
keywords[3].score	0.09012335538864136
keywords[3].display_name	Computer science
keywords[4].id	https://openalex.org/keywords/telecommunications
keywords[4].score	0.08673381805419922
keywords[4].display_name	Telecommunications
language	en
locations[0].id	doi:10.29020/nybg.ejpam.v18i3.6275
locations[0].is_oa	True
locations[0].source.id	https://openalex.org/S2764475867
locations[0].source.issn	1307-5543
locations[0].source.type	journal
locations[0].source.is_oa	True
locations[0].source.issn_l	1307-5543
locations[0].source.is_core	True
locations[0].source.is_in_doaj	False
locations[0].source.display_name	European Journal of Pure and Applied Mathematics
locations[0].source.host_organization
locations[0].source.host_organization_name
locations[0].license	cc-by-nc
locations[0].pdf_url	https://www.ejpam.com/index.php/ejpam/article/download/6275/2221
locations[0].version	publishedVersion
locations[0].raw_type	journal-article
locations[0].license_id	https://openalex.org/licenses/cc-by-nc
locations[0].is_accepted	True
locations[0].is_published	True
locations[0].raw_source_name	European Journal of Pure and Applied Mathematics
locations[0].landing_page_url	https://doi.org/10.29020/nybg.ejpam.v18i3.6275
indexed_in	crossref
authorships[0].author.id	https://openalex.org/A5040027301
authorships[0].author.orcid	https://orcid.org/0000-0003-0006-1156
authorships[0].author.display_name	Muhammad Sajjad
authorships[0].countries	PK
authorships[0].affiliations[0].institution_ids	https://openalex.org/I4210143942
authorships[0].affiliations[0].raw_affiliation_string	National University of Technology (NUTECH), Islamabad, Pakistan
authorships[0].institutions[0].id	https://openalex.org/I4210143942
authorships[0].institutions[0].ror	https://ror.org/05e21fw44
authorships[0].institutions[0].type	education
authorships[0].institutions[0].lineage	https://openalex.org/I4210143942
authorships[0].institutions[0].country_code	PK
authorships[0].institutions[0].display_name	National University of Technology
authorships[0].author_position	first
authorships[0].raw_author_name	Muhammad Sajjad
authorships[0].is_corresponding	False
authorships[0].raw_affiliation_strings	National University of Technology (NUTECH), Islamabad, Pakistan
authorships[1].author.id	https://openalex.org/A5019549124
authorships[1].author.orcid	https://orcid.org/0000-0001-7728-9752
authorships[1].author.display_name	Rafiq Asghar
authorships[1].countries	PK
authorships[1].affiliations[0].institution_ids	https://openalex.org/I12469534
authorships[1].affiliations[0].raw_affiliation_string	Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan
authorships[1].institutions[0].id	https://openalex.org/I12469534
authorships[1].institutions[0].ror	https://ror.org/04s9hft57
authorships[1].institutions[0].type	education
authorships[1].institutions[0].lineage	https://openalex.org/I12469534
authorships[1].institutions[0].country_code	PK
authorships[1].institutions[0].display_name	Quaid-i-Azam University
authorships[1].author_position	middle
authorships[1].raw_author_name	Rida Asghar
authorships[1].is_corresponding	False
authorships[1].raw_affiliation_strings	Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan
authorships[2].author.id	https://openalex.org/A5119151837
authorships[2].author.orcid
authorships[2].author.display_name	Mushtaq K. Abdalrahem
authorships[2].affiliations[0].raw_affiliation_string	College of Pharmacy, University of Al-Ameed
authorships[2].author_position	middle
authorships[2].raw_author_name	Mushtaq K. Abdalrahem
authorships[2].is_corresponding	False
authorships[2].raw_affiliation_strings	College of Pharmacy, University of Al-Ameed
authorships[3].author.id	https://openalex.org/A5119151838
authorships[3].author.orcid
authorships[3].author.display_name	Adnan Burhan Rajab
authorships[3].affiliations[0].raw_affiliation_string	Department of Computer Engineering, College of Engineering, Knowledge University, Erbil 12 44001, Iraq
authorships[3].author_position	middle
authorships[3].raw_author_name	Adnan Burhan Rajab
authorships[3].is_corresponding	False
authorships[3].raw_affiliation_strings	Department of Computer Engineering, College of Engineering, Knowledge University, Erbil 12 44001, Iraq
authorships[4].author.id	https://openalex.org/A5111707655
authorships[4].author.orcid
authorships[4].author.display_name	M. Narayana
authorships[4].countries	JM
authorships[4].affiliations[0].institution_ids	https://openalex.org/I4210129319
authorships[4].affiliations[0].raw_affiliation_string	Department of Mathematics, The University of the West Indies, Kingston 7, Jamaica
authorships[4].institutions[0].id	https://openalex.org/I4210129319
authorships[4].institutions[0].ror	https://ror.org/03fkc8c64
authorships[4].institutions[0].type	education
authorships[4].institutions[0].lineage	https://openalex.org/I137799390, https://openalex.org/I4210129319
authorships[4].institutions[0].country_code	JM
authorships[4].institutions[0].display_name	University of the West Indies
authorships[4].author_position	middle
authorships[4].raw_author_name	Mahesha Narayana
authorships[4].is_corresponding	False
authorships[4].raw_affiliation_strings	Department of Mathematics, The University of the West Indies, Kingston 7, Jamaica
authorships[5].author.id	https://openalex.org/A5119151839
authorships[5].author.orcid
authorships[5].author.display_name	Moin-ud-Din Junjua
authorships[5].countries	CN
authorships[5].affiliations[0].institution_ids	https://openalex.org/I135237710
authorships[5].affiliations[0].raw_affiliation_string	School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China
authorships[5].institutions[0].id	https://openalex.org/I135237710
authorships[5].institutions[0].ror	https://ror.org/01vevwk45
authorships[5].institutions[0].type	education
authorships[5].institutions[0].lineage	https://openalex.org/I135237710
authorships[5].institutions[0].country_code	CN
authorships[5].institutions[0].display_name	Zhejiang Normal University
authorships[5].author_position	middle
authorships[5].raw_author_name	Moin-ud-Din Junjua
authorships[5].is_corresponding	False
authorships[5].raw_affiliation_strings	School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China
authorships[6].author.id	https://openalex.org/A5046464125
authorships[6].author.orcid	https://orcid.org/0000-0003-1233-1774
authorships[6].author.display_name	Salman A. AlQahtani
authorships[6].countries	SA
authorships[6].affiliations[0].institution_ids	https://openalex.org/I28022161
authorships[6].affiliations[0].raw_affiliation_string	New Emerging Technologies and 5G Network and Beyond Research Chair, Department of Computer Engineering, College of Computer and Information Sciences, King Saud University, Riyadh, Saudi Arabia
authorships[6].institutions[0].id	https://openalex.org/I28022161
authorships[6].institutions[0].ror	https://ror.org/02f81g417
authorships[6].institutions[0].type	education
authorships[6].institutions[0].lineage	https://openalex.org/I28022161
authorships[6].institutions[0].country_code	SA
authorships[6].institutions[0].display_name	King Saud University
authorships[6].author_position	last
authorships[6].raw_author_name	Salman A. AlQahtani
authorships[6].is_corresponding	False
authorships[6].raw_affiliation_strings	New Emerging Technologies and 5G Network and Beyond Research Chair, Department of Computer Engineering, College of Computer and Information Sciences, King Saud University, Riyadh, Saudi Arabia
has_content.pdf	True
has_content.grobid_xml	True
is_paratext	False
open_access.is_oa	True
open_access.oa_url	https://www.ejpam.com/index.php/ejpam/article/download/6275/2221
open_access.oa_status	diamond
open_access.any_repository_has_fulltext	False
created_date	2025-10-10T00:00:00
display_name	Design and Analysis of Shortened Bose-Chaudhuri-Hocquenghem Codes for Efficient Data Transmission over the Eisenstein Fields
has_fulltext	False
is_retracted	False
updated_date	2025-11-06T03:46:38.306776
primary_topic.id	https://openalex.org/T11130
primary_topic.field.id	https://openalex.org/fields/17
primary_topic.field.display_name	Computer Science
primary_topic.score	0.9977999925613403
primary_topic.domain.id	https://openalex.org/domains/3
primary_topic.domain.display_name	Physical Sciences
primary_topic.subfield.id	https://openalex.org/subfields/1702
primary_topic.subfield.display_name	Artificial Intelligence
primary_topic.display_name	Coding theory and cryptography
related_works	https://openalex.org/W4391375266, https://openalex.org/W1979597421, https://openalex.org/W2007980826, https://openalex.org/W2061531152, https://openalex.org/W3002753104, https://openalex.org/W2077600819, https://openalex.org/W2142036596, https://openalex.org/W2072657027, https://openalex.org/W2962838298, https://openalex.org/W2600246793
cited_by_count	0
locations_count	1
best_oa_location.id	doi:10.29020/nybg.ejpam.v18i3.6275
best_oa_location.is_oa	True
best_oa_location.source.id	https://openalex.org/S2764475867
best_oa_location.source.issn	1307-5543
best_oa_location.source.type	journal
best_oa_location.source.is_oa	True
best_oa_location.source.issn_l	1307-5543
best_oa_location.source.is_core	True
best_oa_location.source.is_in_doaj	False
best_oa_location.source.display_name	European Journal of Pure and Applied Mathematics
best_oa_location.source.host_organization
best_oa_location.source.host_organization_name
best_oa_location.license	cc-by-nc
best_oa_location.pdf_url	https://www.ejpam.com/index.php/ejpam/article/download/6275/2221
best_oa_location.version	publishedVersion
best_oa_location.raw_type	journal-article
best_oa_location.license_id	https://openalex.org/licenses/cc-by-nc
best_oa_location.is_accepted	True
best_oa_location.is_published	True
best_oa_location.raw_source_name	European Journal of Pure and Applied Mathematics
best_oa_location.landing_page_url	https://doi.org/10.29020/nybg.ejpam.v18i3.6275
primary_location.id	doi:10.29020/nybg.ejpam.v18i3.6275
primary_location.is_oa	True
primary_location.source.id	https://openalex.org/S2764475867
primary_location.source.issn	1307-5543
primary_location.source.type	journal
primary_location.source.is_oa	True
primary_location.source.issn_l	1307-5543
primary_location.source.is_core	True
primary_location.source.is_in_doaj	False
primary_location.source.display_name	European Journal of Pure and Applied Mathematics
primary_location.source.host_organization
primary_location.source.host_organization_name
primary_location.license	cc-by-nc
primary_location.pdf_url	https://www.ejpam.com/index.php/ejpam/article/download/6275/2221
primary_location.version	publishedVersion
primary_location.raw_type	journal-article
primary_location.license_id	https://openalex.org/licenses/cc-by-nc
primary_location.is_accepted	True
primary_location.is_published	True
primary_location.raw_source_name	European Journal of Pure and Applied Mathematics
primary_location.landing_page_url	https://doi.org/10.29020/nybg.ejpam.v18i3.6275
publication_date	2025-08-01
publication_year	2025
referenced_works_count	0
abstract_inverted_index.a	31, 38, 117, 178
abstract_inverted_index.an	138
abstract_inverted_index.as	116
abstract_inverted_index.by	146
abstract_inverted_index.in	53, 106, 133, 165
abstract_inverted_index.is	114, 121, 131
abstract_inverted_index.of	34, 51, 62, 73, 79, 108, 126, 149, 157, 162
abstract_inverted_index.on	3, 18
abstract_inverted_index.to	87, 99, 141, 154, 167, 187
abstract_inverted_index.BCH	64, 190
abstract_inverted_index.BMA	113
abstract_inverted_index.The	56, 111, 135, 170
abstract_inverted_index.and	6, 45, 76, 96, 104, 159, 183, 197
abstract_inverted_index.are	85, 200
abstract_inverted_index.for	8, 42, 49, 123
abstract_inverted_index.low	198
abstract_inverted_index.the	4, 14, 19, 60, 67, 71, 77, 89, 93, 97, 124, 142, 147, 155, 160, 168, 174, 188
abstract_inverted_index.BMA.	169
abstract_inverted_index.This	0
abstract_inverted_index.best	90
abstract_inverted_index.cope	100
abstract_inverted_index.form	37
abstract_inverted_index.have	46
abstract_inverted_index.over	13, 66, 192
abstract_inverted_index.show	172
abstract_inverted_index.that	120, 173
abstract_inverted_index.when	195
abstract_inverted_index.with	23, 59, 70, 101
abstract_inverted_index.work	57
abstract_inverted_index.(BCH)	11
abstract_inverted_index.(BMA)	22
abstract_inverted_index.These	83
abstract_inverted_index.Thus,	27
abstract_inverted_index.based	17
abstract_inverted_index.being	30
abstract_inverted_index.codes	12, 44, 65, 84, 176, 191
abstract_inverted_index.error	102, 180
abstract_inverted_index.field	128
abstract_inverted_index.leads	153
abstract_inverted_index.noisy	54
abstract_inverted_index.offer	177
abstract_inverted_index.study	78
abstract_inverted_index.terms	144
abstract_inverted_index.which	130, 152
abstract_inverted_index.words	94
abstract_inverted_index.better	47
abstract_inverted_index.faster	184
abstract_inverted_index.fields	69, 194
abstract_inverted_index.finite	193
abstract_inverted_index.higher	150, 179
abstract_inverted_index.length	95
abstract_inverted_index.level,	151
abstract_inverted_index.starts	58
abstract_inverted_index.ability	98
abstract_inverted_index.article	1
abstract_inverted_index.balance	91
abstract_inverted_index.between	92
abstract_inverted_index.certain	80
abstract_inverted_index.classes	148
abstract_inverted_index.defined	145
abstract_inverted_index.fields,	16, 29, 36
abstract_inverted_index.focuses	2
abstract_inverted_index.latency	199
abstract_inverted_index.mention	72
abstract_inverted_index.natural	32
abstract_inverted_index.nature.	134
abstract_inverted_index.provide	88
abstract_inverted_index.variety	107
abstract_inverted_index.Gaussian	35
abstract_inverted_index.approach	140
abstract_inverted_index.compared	186
abstract_inverted_index.concerns	137
abstract_inverted_index.contrast	166
abstract_inverted_index.decoding	7, 25, 118
abstract_inverted_index.designed	86
abstract_inverted_index.desired.	201
abstract_inverted_index.equipped	122
abstract_inverted_index.improved	24, 139
abstract_inverted_index.modified	112
abstract_inverted_index.proposed	175
abstract_inverted_index.residual	143
abstract_inverted_index.Algorithm	21
abstract_inverted_index.Shortened	9
abstract_inverted_index.algebraic	40, 81
abstract_inverted_index.channels.	55
abstract_inverted_index.detection	103
abstract_inverted_index.different	132
abstract_inverted_index.generator	74
abstract_inverted_index.mechanism	119
abstract_inverted_index.numerical	163
abstract_inverted_index.presented	115
abstract_inverted_index.reduction	161
abstract_inverted_index.shortened	63
abstract_inverted_index.structure	41
abstract_inverted_index.Eisenstein	15, 28, 68, 127
abstract_inverted_index.arithmetic	129
abstract_inverted_index.capability	182
abstract_inverted_index.complexity	164
abstract_inverted_index.correcting	181
abstract_inverted_index.correction	105
abstract_inverted_index.definition	61
abstract_inverted_index.efficiency	156
abstract_inverted_index.imitations	171
abstract_inverted_index.parameters	48
abstract_inverted_index.computation	185
abstract_inverted_index.convergence	158
abstract_inverted_index.information	52
abstract_inverted_index.polynomials	75
abstract_inverted_index.reliability	196
abstract_inverted_index.traditional	189
abstract_inverted_index.translation	125
abstract_inverted_index.constructing	5
abstract_inverted_index.modification	136
abstract_inverted_index.performance.	26
abstract_inverted_index.transmission	50
abstract_inverted_index.well-devised	39
abstract_inverted_index.applications.	110
abstract_inverted_index.generalization	33
abstract_inverted_index.high-efficiency	109
abstract_inverted_index.Berlekamp-Massey	20
abstract_inverted_index.characteristics.	82
abstract_inverted_index.error-correcting	43
abstract_inverted_index.Bose-Chaudhuri-Hocquenghem	10
cited_by_percentile_year
countries_distinct_count	4
institutions_distinct_count	7
citation_normalized_percentile.value	0.1392518
citation_normalized_percentile.is_in_top_1_percent	False
citation_normalized_percentile.is_in_top_10_percent	True