New Linear Codes Over $\backslash bbF\_\{3\}$ and $\backslash bbF\_\{5\}$and Improvements on Bounds

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• 作者：Siap ; Irfan ; Ray Chaudhuri ; Dijen K.
• 关键词：Quasi cyclic codes ; nearly quasi cyclic codes ; new codes ; improved bounds
• 刊名：Designs, Codes and Cryptography
• 出版年：2000
• 出版时间：2000
• 年：2000
• 卷：21
• 期：1/3
• 页码：223-233
• 全文大小：58 KB

文摘

Oneof the most important problems of coding theory is to constructcodes with best possible minimum distances. In this paper, wegeneralize the method introduced by harada and obtain new codeswhich improve the best known minimum distance bounds of somelinear codes. We have found a new linear ternary code and $8$new linear codes over $\backslash bbF\_\{5\}$ with improved minimumdistances. First we introduce a generalized version of Gray map,then we give definition of quasi cyclic codes and introduce nearlyquasi cyclic codes. Next, we give the parameters of new codeswith their generator matrices. Finally, we have included twotables which give Hamming weight enumerators of these new codes.