Some Constant Weight Codes from Primitive Permutation Groups

Some Constant Weight Codes from Primitive Permutation Groups

In recent years the detailed study of the construction of constant weight codes has been extended from length at most 28 to lengths less than 64. Andries Brouwer maintains web pages with tables of the best known constant weight codes of these lengths. In many cases the codes have more codewords than the best code in the literature, and are not particularly easy to improve. Many of the codes are...

Distinguishing Primitive Permutation Groups

Let G be a permutation group acting on a set V . A partition π of V is distinguishing if the only element of G that fixes each cell of π is the identity. The distinguishing number of G is the minimum number of cells in a distinguishing partition. We prove that if G is a primitive permutation group and |V | ≥ 336, its distinguishing number is two.

Some new distance-4 constant weight codes

Improved binary constant weight codes with minimum distance 4 and length at most 28 are constructed. A table with bounds on the chromatic number of small Johnson graphs is given.

Factorizations of Primitive Permutation Groups

Error-correcting codes from permutation groups

We replace the usual setting for error-correcting codes (i.e. vector spaces over finite fields) with that of permutation groups. We give an algorithm which uses a combinatorial structure which we call an uncovering-by-bases, related to covering designs, and construct some examples of these. We also analyse the complexity of the algorithm. We then formulate a conjecture about uncoverings-by-base...