HIGHER WEIGHTS AND GENERALIZED MDS CODES

Higher Weights of Grassmann Codes

Using a combinatorial approach to studying the hyperplane sections of Grassmannians, we give two new proofs of a result of Nogin concerning the higher weights of Grassmann codes. As a consequence, we obtain a bound on the number of higher dimensional subcodes of the Grassmann code having the minimum Hamming norm. We also discuss a generalization of Grassmann codes .

Higher Weights and Binary Self-Dual Codes

The theory of higher weights is applied to binary self-dual codes. Bounds are given for the second minimum higher weight and a Gleason type theorem is derived for the second higher weight enumerator. The second weight enumerator is shown to be unique for the putative 72; 36; 16] Type II code and the rst three minimum weights are computed for optimal codes of length less than 28. We connect them...

New MDS Self-Dual Codes from Generalized Reed-Solomon Codes

Both MDS and Euclidean self-dual codes have theoretical and practical importance and the study of MDS self-dual codes has attracted lots of attention in recent years. In particular, determining existence of q-ary MDS self-dual codes for various lengths has been investigated extensively. The problem is completely solved for the case where q is even. The current paper focuses on the case where q ...

On generalized weights for codes over ℤk

Generalized Hamming weights for linear codes

Error control codes are widely used to increase the reliability of transmission of information over various forms of communications channels. The Hamming weight of a codeword is the number of nonzero entries in the word; the weights of the words in a linear code determine the error-correcting capacity of the code. The rth generalized Hamming weight for a linear code C, denoted by dr(C), is the ...