Andries E Brouwer,Sven C Polak
Andries E Brouwer
For n , d , w ∈ N , let A(n, d, w) denote the maximum size of a binary code of word length n, minimum distance d and constant weight w. Schrijver recently showed using semidefinite programming that A ( 23 , 8 , 11 ) = 1288 , and the...
Sven C Polak
Sven C Polak
For q , n , d ∈ N , let A q ( n , d ) be the maximum size of a code C ⊆ [ q ] n with minimum distance at least d. We give a divisibility argument resulting in the new upper bounds A 5 ( 8 , 6 ) ≤ 65 , A 4 ( 11 , 8...
Arnold Neumaier
Arnold Neumaier
The paper describes improved analysis techniques for basis reduction that allow one to prove strong complexity bounds and reduced basis guarantees for traditional reduction algorithms and some of their variants. This is achieved by a carefu...
Bart Litjens,Sven Polak,Alexander Schrijver
Bart Litjens
For nonnegative integers q, n, d, let A q ( n , d ) denote the maximum cardinality of a code of length n over an alphabet [q] with q letters and with minimum distance at least d. We consider the following upper bound on A q ( n , d ) ...