CONSTRUCTION FOR SELF-ORTHOGONAL CODES OVER A CERTAIN NON-CHAIN FROBENIUS RING

Boran Kim

doi:10.4134/JKMS.j210357

CONSTRUCTION FOR SELF-ORTHOGONAL CODES OVER A CERTAIN NON-CHAIN FROBENIUS RING

Boran Kim

Department of Mathematics Education

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We present construction methods for free self-orthogonal (self-dual or Type II) codes over Z4[v]=hv2 + 2vi which is one of the finite commutative local non-chain Frobenius rings of order 16. By considering their Gray images on Z4, we give a construct method for a code over Z4. We have some new and optimal codes over Z4 with respect to the minimum Lee weight or minimum Euclidean weight.

Original language	English
Pages (from-to)	193-204
Number of pages	12
Journal	Journal of the Korean Mathematical Society
Volume	59
Issue number	1
DOIs	https://doi.org/10.4134/JKMS.j210357
State	Published - 2022

Keywords

Code over Z4
Frobenius ring
Non-chain ring
Optimal code
Self-orthogonal code

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10.4134/JKMS.j210357

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title = "CONSTRUCTION FOR SELF-ORTHOGONAL CODES OVER A CERTAIN NON-CHAIN FROBENIUS RING",

abstract = "We present construction methods for free self-orthogonal (self-dual or Type II) codes over Z4[v]=hv2 + 2vi which is one of the finite commutative local non-chain Frobenius rings of order 16. By considering their Gray images on Z4, we give a construct method for a code over Z4. We have some new and optimal codes over Z4 with respect to the minimum Lee weight or minimum Euclidean weight.",

keywords = "Code over Z4, Frobenius ring, Non-chain ring, Optimal code, Self-orthogonal code",

author = "Boran Kim",

note = "Publisher Copyright: {\textcopyright} 2022 Korean Mathematical Society.",

year = "2022",

doi = "10.4134/JKMS.j210357",

language = "English",

volume = "59",

pages = "193--204",

journal = "Journal of the Korean Mathematical Society",

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AU - Kim, Boran

PY - 2022

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N2 - We present construction methods for free self-orthogonal (self-dual or Type II) codes over Z4[v]=hv2 + 2vi which is one of the finite commutative local non-chain Frobenius rings of order 16. By considering their Gray images on Z4, we give a construct method for a code over Z4. We have some new and optimal codes over Z4 with respect to the minimum Lee weight or minimum Euclidean weight.

AB - We present construction methods for free self-orthogonal (self-dual or Type II) codes over Z4[v]=hv2 + 2vi which is one of the finite commutative local non-chain Frobenius rings of order 16. By considering their Gray images on Z4, we give a construct method for a code over Z4. We have some new and optimal codes over Z4 with respect to the minimum Lee weight or minimum Euclidean weight.

KW - Code over Z4

KW - Frobenius ring

KW - Non-chain ring

KW - Optimal code

KW - Self-orthogonal code

UR - https://www.scopus.com/pages/publications/85122965587

U2 - 10.4134/JKMS.j210357

DO - 10.4134/JKMS.j210357

M3 - Article

AN - SCOPUS:85122965587

SN - 0304-9914

VL - 59

SP - 193

EP - 204

JO - Journal of the Korean Mathematical Society

JF - Journal of the Korean Mathematical Society

IS - 1

ER -

CONSTRUCTION FOR SELF-ORTHOGONAL CODES OVER A CERTAIN NON-CHAIN FROBENIUS RING

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Keywords

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