Optimal constant weight covering codes and nonuniform group divisible 3-designs with block size four

Authors:
Xiande Zhang;Hui Zhang;Gennian Ge
Affiliations:
Department of Mathematics, Zhejiang University, Hangzhou, People's Republic of China 310027;Department of Mathematics, Zhejiang University, Hangzhou, People's Republic of China 310027;Department of Mathematics, Zhejiang University, Hangzhou, People's Republic of China 310027
Venue:
Designs, Codes and Cryptography
Year:
2012

Citing 5
Cited 0

Covering triples by quadruples: an asymptotic solution

Journal of Combinatorial Theory Series A
Subdesigns in Steiner quadruple systems

Journal of Combinatorial Theory Series A
Bounds on the sizes of constant weight covering codes

Designs, Codes and Cryptography
On group divisible covering designs

Discrete Mathematics
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)

Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)

Quantified Score

Hi-index	0.00

Visualization

Abstract

Let K q (n, w, t, d) be the minimum size of a code over Z q of length n, constant weight w, such that every word with weight t is within Hamming distance d of at least one codeword. In this article, we determine K q (n, 4, 3, 1) for all n 驴 4, q = 3, 4 or q = 2 m + 1 with m 驴 2, leaving the only case (q, n) = (3, 5) in doubt. Our construction method is mainly based on the auxiliary designs, H-frames, which play a crucial role in the recursive constructions of group divisible 3-designs similar to that of candelabra systems in the constructions of 3-wise balanced designs. As an application of this approach, several new infinite classes of nonuniform group divisible 3-designs with block size four are also constructed.