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On symbol-pair weight distribution of MDS codes and simplex codes over finite fields

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Symbol-pair code is a new coding framework proposed to combat pair-errors in symbol-pair read channels. Remarkably, a classical maximum distance separable (MDS) code is also an MDS symbol-pair code. In… Click to show full abstract

Symbol-pair code is a new coding framework proposed to combat pair-errors in symbol-pair read channels. Remarkably, a classical maximum distance separable (MDS) code is also an MDS symbol-pair code. In this paper, we investigate the symbol-pair weight distribution of MDS codes and the symbol b -weight distribution of simplex codes over finite fields respectively. Surprisingly, one can derive that all the nonzero codewords of simplex codes have the same symbol b -weight and rearrangement of coordinates in simplex codes may induce different symbol-pair weights. Moreover, the symbol b -weight distribution of variation simplex codes over certain finite fields is determined.

Keywords: weight distribution; simplex codes; symbol pair; pair

Journal Title: Cryptography and Communications
Year Published: 2021

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