Constructions of binary constant-weight cyclic codes and cyclically permutable codes

Constructions for optimal constant weight cyclically permutable codes and difference families

A cyclically permutable code is a binary code whose codewords are cyclically distinct and have full cyclic order. An important class of these codes are the constant weight cyclically permutable codes. In a code of this class all codewords have the same weight w. These codes have many applications, including in optical code-division multiple-access communication systems and in constructing proto...

Optimal (v, 3, 1) binary cyclically permutable constant weight codes with small v

We classify up to multiplier equivalence optimal (v, 3, 1) binary cyclically permutable constant weight (CPCW) codes with v ≤ 61. There is a one-to-one correspondence between optimal (v, 3, 1) CPCW codes, optimal cyclic binary constant weight codes with weight 3 and minimal distance 4, (v, 3; b(v − 1)/6c) difference packings, and optimal (v, 3, 1) optical orthogonal codes. Therefore the classif...

Cyclically permutable codes

Brevity is the soul of wit. William Shakespeare A cyclically permutable code is a set of codewords having the property that no codeword is a cyclic shift of another codeword. We study the problem of constructing cyclically permutable codes of large size and low correlation. Cyclically permutable codes are used in code-division multiple-access systems realized by e.g. direct-sequence modulation ...

On the Grobner Basis of a Family of Quasi-Cyclic LDPC Codes

A new table of constant weight codes

A table of binary constant weight codes of length n <; 28 is presented. Explicit constructions are given for most of the 600 codes in the table; the majority of these codes are new. The known techniques for constructing constant weight codes are surveyed, and also a table is given of (unrestricted) binary codes of length J1 <; 28.