Abstract
Let Fq be a finite field with q elements, l an odd prime, and t,v positive integers such that lv|(q−1) and gcd(t,l)=1. In this paper, we give a combinatorial result and use it to determine the weight distribution of a cyclic code of length tlm with t|(q−1), which is an open question in Yang et al. (2013). Moreover we compute the weight distributions of cyclic codes of length tlm, where q≡3(mod4) and t=4 or 8.
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