On traceability property of equidistant codes

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• 作者：Anu Kathuria^a ; ^{anu_sept24@rediffmail.com} ; S.K. Arora^b ; Sudhir Batra^c ; ^{batrasudhir@rediffmail.com}
• 关键词：Maximum Distance Separable (MDS) code ; Equidistant code ; Traceable (TA) code ; Jabobsthal matrix ; Hadamard matrix ; RS code
• 刊名：Discrete Mathematics
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：340
• 期：4
• 页码：713-721
• 全文大小：406 K
• 卷排序：340

文摘

Necessary and Sufficient conditions for an equidistant code to be a 2-TA code are obtained. An explicit construction method is proposed to obtain linear MDS [p+1,2,p][p+1,2,p] codes over the finite field FpFp, where pp is a prime. These codes can be used as 2-TA codes for p>2p>2. In particular, for p=3p=3, it is observed that the linear [4, 2, 3] MDS code contradicts a result of Jin and Blaum (2007). The correct version of this result and its proof is given. Existence of some infinite families of equidistant 2-TA codes is shown by using Jacobsthal and Hadamard matrices. Some of these codes are also observed to be good equidistant code (Sinha et al., 2008).