An armstrong(q, k, n) code is a q-ary code of length n of minimum distance n - k + 1 such that for every (k - 1)-subset of coordinates there exists a pair of codewords that agree exactly there. Let f (q, k) denote the...
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(纸本)9781665402873
An armstrong(q, k, n) code is a q-ary code of length n of minimum distance n - k + 1 such that for every (k - 1)-subset of coordinates there exists a pair of codewords that agree exactly there. Let f (q, k) denote the largest n such that an armstrong(q, k, n) code exists. Upper and lower bounds on f (q, k) were given earlier in general, and in the case when k > k(0)(q). In the present paper we propose a new construction to provide armstrong((p +1)/2, 2l, p) for a prime p and give an upper bound in the case of fixed k and large enough q. Both results imply improvements on corresponding general known bounds for large enough q.
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