Abstract

For an odd integer B 0 mod(3) and for a cyclotomic coset C of integers modulo B having the property: if r ε C , then B — r ε C ; the number of integers which belong to C and to the half-open interval ( B /3, 2 B /3 is lower bounded. This result is then used to obtain a lower bound on the minimum arithmetic distance of a cyclic AN -code with generator A and length n whenever B = (2 n −1)/ A is not divisible by 3 and B |2 q + 1 for some integer q .

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