Equidistant Arithmetic Codes and Character Sums
نویسنده
چکیده
A cyclic arithmetic code is a subgroup of Z/(rn − 1)Z, where the weight of a word x is the minimal number of nonzero coefficients in the representation x ≡ ∑n−1 i=0 cir with |ci| < r for all i. A code is called equidistant if all codewords have the same weight. In this paper necessary conditions for the existence of equidistant codes are given. By relating these conditions to character sums on certain intervals, it is shown that for r = 2, 3 no new equidistant codes exist, and several infinite families of equidistant codes are given.
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تاریخ انتشار 1994