On (q, 1)-subnormal q-ary covering codes

New Constructions for q-ary Covering Codes

Upper bounds on Kq (n; R), the minimum number of codewords in a q-ary code of length n and covering radius R, are improved. Such bounds are obtained by constructing corresponding covering codes. In particular, codes of length q + 1 are discussed. Good such codes can be obtained from maximum distance separable (MDS) codes. Furthermore, they can often be combined eeectively with other covering co...

A note on bounds for q-ary covering codes

Two strongly seminormal codes over 2s are constructed to prove a conjecture of Ostergard. It is shown that a result of Honkala on ( I C , t)-subnormal codes holds also under weaker assumptions. A lower bound and an upper bound on Kq(n, R), the minimal cardinality of a q-ary code of length n with covering radius R are obtained. These give improvements in seven upper bounds and twelve lower bound...

Lower Bounds for q-ary Codes with Large Covering Radius

Let Kq(n,R) denote the minimal cardinality of a q-ary code of length n and covering radius R. Recently the authors gave a new proof of a classical lower bound of Rodemich on Kq(n, n−2) by the use of partition matrices and their transversals. In this paper we show that, in contrast to Rodemich’s original proof, the method generalizes to lower-bound Kq(n, n − k) for any k > 2. The approach is bes...

Nonequivalent q-ary Perfect Codes

Prefixless q-ary Balanced Codes

We will present a Knuth-like method for balancing q-ary codewords, which is characterized by the absence of a prefix that carries the information on the balancing index. Lookup tables for coding and decoding the prefix are avoided. Index Terms Constrained code, balanced code, running digital sum, Knuth code, error correction.