Weight distribution of cyclic codes with arbitrary number of generalized Niho type zeroes with corrigendum
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Cyclic codes are an important class of linear codes, whose weight distribution have been extensively studied. Most previous results obtained so far were for cyclic codes with no more than three zeroes. Inspired by the works Li-Zeng-Hu and gegeng2, we study two families of cyclic codes over F_p with arbitrary number of zeroes of generalized Niho type, more precisely (for p=2) of t+1 zeroes, and (for any prime p) of t zeroes for any t. We find that the first family has at most (2t+1) non-zero weights, and the second has at most 2t non-zero weights. Their weight distribution are also determined in the paper.
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