环GR(4,2)上一类负循环码的Gray象

开晓山;朱士信

系统科学与数学 ›› 2010, Vol. 30 ›› Issue (3) : 334-340.

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系统科学与数学 ›› 2010, Vol. 30 ›› Issue (3) : 334-340. DOI: 10.12341/jssms08948
论文

环GR(4,2)上一类负循环码的Gray象

    开晓山, 朱士信
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Gray Images of a Class of Negacyclic Codes over GR(4,2)

    KAI Xiaoshan, ZHU Shixin
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摘要

研究了GR(4,2)上长为2s的负循环码的Gray象,证明了GR(4,2)上长为2s的负循环码的Gray象是F4上长为2s+2指数为2的准循环码. 通过计算GR(2a,m)上长为2s的负循环码的齐次距离, 确定了GR(4,2)上长为2s的负循环码的Gray象的汉明距离.

Abstract

This paper investigates the Gray images of negacyclic codes of length 2s over GR(4,2). It is proved that the Gray image of a negacyclic code of length 2s over GR(4,2) is a distance-invariant linear quasicyclic code of index 2 and length 2s+2 over F4. The homogeneous distances of negacyclic codes of length 2s over GR(2a,m) in general are calculated. The homogeneous distances are used to determine the Hamming distances of the Gray images of negacyclic codes of length 2s over GR(4,2).

关键词

Gray象 / 汉明距离 / 齐次距离 / 负循环码 / 准循环码.

Key words

Gray map / Hamming distance / homogeneous distance / negacyclic codes / quasicyclic codes.

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开晓山 , 朱士信. 环GR(4,2)上一类负循环码的Gray象. 系统科学与数学, 2010, 30(3): 334-340. https://doi.org/10.12341/jssms08948
KAI Xiaoshan , ZHU Shixin. Gray Images of a Class of Negacyclic Codes over GR(4,2). Journal of Systems Science and Mathematical Sciences, 2010, 30(3): 334-340 https://doi.org/10.12341/jssms08948
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