## Pairs of Codes with Prescribed Hamming Distances and Coincidences

### Authors: Vince Grolmusz

ABSTRACT

In this work we describe a fast algorithm for generating pairs of q-ary codes with prescribed pairwise Hamming-distances and coincidences (for a letter $s\in\{0,1,\ldots,q-1\}$, the number of $s$-coincidences between codewords $a$ and $b$ is the number of letters $s$ in the same positions both in $a$ and $b$). The method is a generalization of a method for constructing set-systems with prescribed intersection sizes (V. Grolmusz: Constructing Set-Systems with Prescribed Intersection Sizes, DIMACS Technical Report No. 2001-03), where only the case $q=2$ and $s=1$ was examined. We also generate codes with prescribed $k$-wise coincidences and Hamming-distances.

Paper Available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-09.ps.gz