This paper deals with the problem of increasing the minimum distance of a linear code by adding one or more columns to the generator matrix. We present a simple greedy algorithm which surprisingly yields many codes improving the previously known lower bounds on the minimum distance. We also discuss variations of the algorithm that succeed when the greedy algorithm is not feasible or fails.

Recently, there were several papers on finding good linear codes. Various methods were introduced to make good linear codes. In this paper, we give a simple iterative algorithm to make good linear codes. Using our algorithm we construct 86 codes which improve the minimum distance of previously best known linear codes for fixed parametersn,k.

Our purpose is to find an upper bound for the length of ans-extremal code over F2(resp. F4) when d equiv 2 (mod 4) (resp. d odd). This question is left open in [A bound for certain s -extremal lattices and codes, Archiv der Mathematik, vol. 89, no. 2, pp. 143-151, 2007] (resp. [s-extremal additive F4codes, Advances in Mathematics of Communications, vol. 1, no. 1, pp. 111-130,2007]). More precisely, we show that if there is an [n, n/2, d]s-extremal Type I binary self-dual code with d > 6 and d equiv 2 (mod 4), then n1 and d, equiv 1 (mod 2), then n2+ uF2and derive an upper bound for the length of an .s-extremal self-dual code over F2+ uF2using the information on binarys-extremal codes.