Optimal cyclic codes with generalized Niho type zeroes and the weight distribution
Abstract
In this paper we extend the works gegeng2,XLZD further in two directions and compute the weight distribution of these cyclic codes under more relaxed conditions. It is interesting to note that many cyclic codes in the family are optimal and have only a few non-zero weights. Besides using similar ideas from gegeng2,XLZD, we carry out some subtle manipulation of certain exponential sums.
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