Now showing items 1-10 of 66
The sizes of optimal q-ary codes of weight three and distance four : a complete solution
This correspondence introduces two new constructive techniques to complete the determination of the sizes of optimal q-ary codes of constant weight three and distance four.
Improved lower bounds for constant GC-content DNA codes
The design of large libraries of oligonucleotides having constant GC-content and satisfying Hamming distance constraints between oligonucleotides and their Watson-Crick complements is important in reducing hybridization ...
The PBD-closure of constant-composition codes
We show an interesting pairwise balanced design (PBD)-closure result for the set of lengths of constant-composition codes whose distance and size meet certain conditions. A consequence of this PBD-closure result is that ...
Constructions for q-ary constant-weight codes
This paper introduces a new combinatorial construction for q-ary constant-weight codes which yields several families of optimal codes and asymptotically optimal codes. The construction reveals intimate connection between ...
Linear size optimal q-ary constant-weight codes and constant-composition codes
An optimal constant-composition or constant-weight code of weight w has linear size if and only if its distance d is at least 2w-1. When d ≥ 2w, the determination of the exact size of such a constant-composition or ...
On component groups of Jo(N) and degeneracy maps
For an integer M >1 and a prime p ≥ 5 not dividing M, we study the kernel of the degeneracy map ΦʳMp,p --˃ ΦMpʳ,p, where ΦMp,p and ΦMpʳ,p are the component groups of J0(Mp) and J0(Mpʳ), respectively. This is then ...
Universal cycles for minimum coverings of pairs by triples, with application to 2-radius sequences
A new ordering, extending the notion of universal cycles of Chung et al. (1992), is proposed for the blocks of k-uniform set systems. Existence of minimum coverings of pairs by triples that possess such an ordering is ...
Cycle systems in the complete bipartite graph plus a one-factor
Let Kn,n denote the complete bipartite graph with n vertices in each partite set and Kn,n+I denote Kn,n with a one-factor added. It is proved in this paper that there exists an m-cycle system ...
Improved p-ary codes and sequence families from Galois rings of characteristic p2
This paper explores the applications of a recent bound on some Weil-type exponential sums over Galois rings in the construction of codes and sequences. A family of codes over Fp, mostly nonlinear, of length pm+1 and size ...
Generalization of Steane’s enlargement construction of quantum codes and applications
We generalize Steane’s enlargement construction of binary quantum codes to q-ary quantum codes. We then apply this result to BCH codes and the study of asymptotic bounds, and obtain improvements to the quantum BCH codes ...