Constructions for $q$-Ary Constant-Weight Codes

New inequalities for $$q$$ q -ary constant-weight codes

Using double counting, we prove Delsarte inequalities for qary codes and their improvements. Applying the same technique to q-ary constant-weight codes, we obtain new inequalities for q-ary constantweight codes.

New Constructions for q-ary Covering Codes

Upper bounds on Kq (n; R), the minimum number of codewords in a q-ary code of length n and covering radius R, are improved. Such bounds are obtained by constructing corresponding covering codes. In particular, codes of length q + 1 are discussed. Good such codes can be obtained from maximum distance separable (MDS) codes. Furthermore, they can often be combined eeectively with other covering co...

Linear Size Optimal q-ary Constant-Weight Codes and Constant-Composition Codes

An optimal constant-composition or constant-weight code of weight has linear size if and only if its distance is at least . When , the determination of the exact size of such a constant-composition or constant-weight code is trivial, but the case of has been solved previously only for binary and ternary constant-composition and constant-weight codes, and for some sporadic instances. This paper ...

On the Constructions of Constant-Weight Codes

NONLINEAR q-ARY CODES: CONSTRUCTIONS AND MINIMUM DISTANCE COMPUTATION

A nonlinear code can be represented as the union of cosets of a linear subcode. Properties and constructions of new codes from given ones in terms of this representation can be described. Algorithms to compute the minimum distance of nonlinear codes, based on known algorithms for linear codes, are also established. Moreover, the performance of these algorithms is studied and an estimation of th...