New Bounds and Constructions for Multiply Constant-Weight Codes

New lower bounds for constant weight codes

with M (which is expected). However, as M increases beyond Ahstrart -Some new lower bounds are given for A(n,4, IV), the maximum number of codewords in a binary code of length n, min imum distance 4, and constant weight IV. In a number of cases the results significantly 1.0 improve on the best bounds previously known. h=O 1 .

New LMRD bounds for constant dimension codes and improved constructions

Let V ∼= Fq be a v-dimensional vector space over the finite field Fq with q elements. By [ V k ] we denote the set of all k-dimensional subspaces in V . Its size is given by the q-binomial coefficient [ v k ]q = ∏k−1 i=0 qv−qi qk−qi for 0 ≤ k ≤ v and 0 otherwise. The set of all subspaces of V forms a metric space associated with the so-called subspace distance dS(U,W ) = dim(U + W ) − dim(U ∩ W...

Upper bounds for constant-weight codes

Let ( ) denote the maximum possible number of codewords in an ( ) constant-weight binary code. We improve upon the best known upper bounds on ( ) in numerous instances for 24 and 12, which is the parameter range of existing tables. Most improvements occur for = 8 10 where we reduce the upper bounds in more than half of the unresolved cases. We also extend the existing tables up to 28 and 14. To...

On the Constructions of Constant-Weight Codes

New Optimal Constant Weight Codes

In 2006, Smith et al. published a new table of constant weight codes, updating existing tables originally created by Brouwer et al. This paper improves upon these results by filling in 9 missing constant weight codes, all of which are optimal by the second Johnson bound. This completes the tables for A(n, 16, 9) and A(n, 18, 10) up to n = 63 and corrects some A(n, 14, 8).