Codes from affine permutation groups (Q1273537)

The maximum cardinality of a (linear or nonlinear) binary code of length \(n\) and minimum Hamming distance \(d\) is denoted by \(A(n,d)\). The author constructs codes that lead to improved lower bounds on \(A(n,d)\). The codes are found by stochastic computer search. A permutation group under which a code is invariant is prescribed before the search. The permutation groups used are mainly affine groups. The new bounds are: \(A(22,10) \geq 50\), \(A(23,10) \geq 76\), \(A(25,10) \geq 166\), \(A(26,10) \geq 270\), \(A(29,10) \geq 1460\), and \(A(28,12) \geq 178\).