## DIMACS TR: 2002-09

## 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

DIMACS Home Page