A Bound for the Maximum Weight of a Linear Code

نویسندگان

Simeon Ball

Aart Blokhuis

چکیده

It is shown that the parameters of a linear code over Fq of length n, dimension k, minimum weight d and maximum weight m satisfy a certain congruence relation. In the case that q = p is a prime, this leads to the bound m ≤ (n−d)p−e(p−1), where e ∈ {0, 1, . . . , k − 2} is maximal with the property that ( n− d e ) 6= 0 (mod pk−1−e). Thus, if C contains a codeword a length n then n ≥ d/(p− 1) + d + e.

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