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

摘要

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 symbolb-weight distribution of simplex codes over finite fields respectively. Surprisingly, one can derive that all the nonzero codewords of simplex codes have the same symbolb-weight and rearrangement of coordinates in simplex codes may induce different symbol-pair weights. Moreover, the symbolb-weight distribution of variation simplex codes over certain finite fields is determined.