New results and bounds on codes over GF (17)

Eric Chen; Nuh Aydin; Fredrik Jönsson; Kamilla Klonowska

doi:10.13069/jacodesmath.v11i1.257

New results and bounds on codes over GF (17)

Eric Chen, Nuh Aydin, Fredrik Jönsson, Kamilla Klonowska

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Determining the best possible values of the parameters of a linear code is one of the most fundamental and challenging problems in coding theory. There exist databases of best-known linear codes (BKLC) over small finite fields. In this work, we establish a database of BKLCs over the field GF (17) together with upper bounds on the minimum distances for lengths up to 150 and dimensions up to 6. In the process, we have found many new linear codes over GF (17).

Originalspråk	Engelska
Sidor (från-till)	27-39
Antal sidor	13
Tidskrift	Journal of Algebra Combinatorics Discrete Structures and Applications
Volym	11
Nummer	1
DOI	https://doi.org/10.13069/jacodesmath.v11i1.257
Status	Publicerad - 2023-okt.-23

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10.13069/jacodesmath.v11i1.257Licens: CC BY

257-Article Text-1327-1-10-20240115Slutlig publicerad version, 577 KBLicens: CC BY

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abstract = "Determining the best possible values of the parameters of a linear code is one of the most fundamental and challenging problems in coding theory. There exist databases of best-known linear codes (BKLC) over small finite fields. In this work, we establish a database of BKLCs over the field GF (17) together with upper bounds on the minimum distances for lengths up to 150 and dimensions up to 6. In the process, we have found many new linear codes over GF (17).",

keywords = "Distance bounds, Lower bounds, Optimal codes, Quasi-cyclic codes, Quasi-twisted codes, Search algorithms for linear codes, Upper bounds",

author = "Eric Chen and Nuh Aydin and Fredrik J{\"o}nsson and Kamilla Klonowska",

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AU - Aydin, Nuh

AU - Jönsson, Fredrik

AU - Klonowska, Kamilla

PY - 2023/10/23

Y1 - 2023/10/23

N2 - Determining the best possible values of the parameters of a linear code is one of the most fundamental and challenging problems in coding theory. There exist databases of best-known linear codes (BKLC) over small finite fields. In this work, we establish a database of BKLCs over the field GF (17) together with upper bounds on the minimum distances for lengths up to 150 and dimensions up to 6. In the process, we have found many new linear codes over GF (17).

AB - Determining the best possible values of the parameters of a linear code is one of the most fundamental and challenging problems in coding theory. There exist databases of best-known linear codes (BKLC) over small finite fields. In this work, we establish a database of BKLCs over the field GF (17) together with upper bounds on the minimum distances for lengths up to 150 and dimensions up to 6. In the process, we have found many new linear codes over GF (17).

KW - Distance bounds

KW - Lower bounds

KW - Optimal codes

KW - Quasi-cyclic codes

KW - Quasi-twisted codes

KW - Search algorithms for linear codes

KW - Upper bounds

U2 - 10.13069/jacodesmath.v11i1.257

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M3 - Article

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JO - Journal of Algebra Combinatorics Discrete Structures and Applications

JF - Journal of Algebra Combinatorics Discrete Structures and Applications

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ER -

New results and bounds on codes over GF (17)

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