473 research outputs found
Coding Theory and Algebraic Combinatorics
This chapter introduces and elaborates on the fruitful interplay of coding
theory and algebraic combinatorics, with most of the focus on the interaction
of codes with combinatorial designs, finite geometries, simple groups, sphere
packings, kissing numbers, lattices, and association schemes. In particular,
special interest is devoted to the relationship between codes and combinatorial
designs. We describe and recapitulate important results in the development of
the state of the art. In addition, we give illustrative examples and
constructions, and highlight recent advances. Finally, we provide a collection
of significant open problems and challenges concerning future research.Comment: 33 pages; handbook chapter, to appear in: "Selected Topics in
Information and Coding Theory", ed. by I. Woungang et al., World Scientific,
Singapore, 201
Constructions of 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 q-ary constant-weight codes and sets of pairwise disjoint combinatorial
designs of various types.Comment: 12 page
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