形式幂级数环上的自对偶码&nbsp;

刘修生, 刘花璐

doi:10.13371/j.cnki.chin.q.j.m.2014.01.005

数学季刊 >

2014 , Vol. 29 >Issue 1: 30 - 38

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2014.01.005

形式幂级数环上的自对偶码

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School of Mathematics and Physics, Hubei Polytechnic University

LIU Xiu-sheng(1960-), male, native of Huangshi, Hubei, a professor of Hubei Polytechnic University, engages in algebra coding.

收稿日期: 2011-12-05

网络出版日期: 2022-11-29

基金资助

Supported by the Scientific Research Foundation of Hubei Provincial Education Department (B2013069)； Supported by the National Science Foundation of Hubei Polytechnic University (12xjz14A,11yjz37B)

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The Self-dual Codes over Formal Power Series Rings

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School of Mathematics and Physics, Hubei Polytechnic University

LIU Xiu-sheng(1960-), male, native of Huangshi, Hubei, a professor of Hubei Polytechnic University, engages in algebra coding.

Received date: 2011-12-05

Online published: 2022-11-29

Supported by

Supported by the Scientific Research Foundation of Hubei Provincial Education Department (B2013069)； Supported by the National Science Foundation of Hubei Polytechnic University (12xjz14A,11yjz37B)

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摘要

The codes of formal power series rings R_{\infty}=\mathbb{F}[[\gamma]]={\Sigma_{l=0}^{\infty}a_{l}\gamma_{l}|a_{l}\in\mathbb{F}} and finite chain rings R_i={a₀+a₁r+…+a_i-1\gamma^i-1|a_i∈\mathbb{F}} have close relationship in lifts and projection. In this paper, we study self-dual codes over R_∞by means of self-dual codes over R_i, and give some characterizations of self-dual codes over R_∞.

关键词： self-dual codes; \gamma-adic codes; projective codes

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刘修生, 刘花璐 . 形式幂级数环上的自对偶码 [J]. 数学季刊, 2014 , 29(1) : 30 -38 . DOI: 10.13371/j.cnki.chin.q.j.m.2014.01.005

Abstract

The codes of formal power series rings R_{\infty}=\mathbb{F}[[\gamma]]=\Sigma_{l=0}^{\infty}a_{l}\gamma_{l}|a_{l}\in\mathbb{F}} and finite chain rings

Ri={a0+a1r+…+ai-1\gamma^i-1|ai∈\mathbb{F}} have close relationship in lifts and projection. In this paper, we study self-dual codes over R∞ by means of self-dual codes over Ri, and give some characterizations of self-dual codes over R∞.

Key words： self-dual codes; 丁-adic codes; projective codes

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