New completely regular q-ary codes based on Kronecker products
Abstract
For any integer $\rho \geq 1$ and for any prime power q, the explicit construction of a infinite family of completely regular (and completely transitive) q-ary codes with d=3 and with covering radius $\rho$ is given. The intersection array is also computed. Under the same conditions, the explicit construction of an infinite family of q-ary uniformly packed codes (in the wide sense) with covering radius $\rho$, which are not completely regular, is also given. In both constructions the Kronecker product is the basic tool that has been used.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2008
- DOI:
- 10.48550/arXiv.0810.4993
- arXiv:
- arXiv:0810.4993
- Bibcode:
- 2008arXiv0810.4993R
- Keywords:
-
- Computer Science - Information Theory;
- Computer Science - Discrete Mathematics;
- Mathematics - Combinatorics;
- 94B25
- E-Print:
- Submitted to IT-IEEE. Theorem 1 in Section III was presented at the 2nd International Castle Meeting on Coding Theory and Applications (2ICMCTA), Medina del Campo, Spain, September 2008.}}