Constructing permutation arrays from groups
نویسندگان
چکیده
منابع مشابه
Constructing permutation arrays from groups
LetM(n, d) be the maximum size of a permutation array on n symbols with pairwise Hamming distance at least d. We use various combinatorial, algebraic, and computational methods to improve lower bounds forM(n, d). We compute the Hamming distances of affine semilinear groups and projective semilinear groups, and unions of cosets of AGL(1, q) and PGL(2, q) with Frobenius maps to obtain new, improv...
متن کاملConstructing transitive permutation groups
This paper presents a new algorithm to classify all transitive subgroups of the symmetric group up to conjugacy. It has been used to determine the transitive groups of degree up to 30.
متن کاملConstructing Permutation Representations for Matrix Groups
New techniques, both theoretical and practical, are presented for constructing permutation representations for computing with matrix groups defined over finite fields. The permutation representation is constructed on a conjugacy class of subgroups of prime order. We construct a base for the permutation representation, which in turn simplifies the computation of a strong generating set. In addit...
متن کاملConstructing error-correcting binary codes using transitive permutation groups
Let A2(n, d) be the maximum size of a binary code of length n and minimum distance d. In this paper we present the following new lower bounds: A2(18, 4) ≥ 5632, A2(21, 4) ≥ 40960, A2(22, 4) ≥ 81920, A2(23, 4) ≥ 163840, A2(24, 4) ≥ 327680, A2(24, 10) ≥ 136, and A2(25, 6) ≥ 17920. The new lower bounds are a result of a systematic computer search over transitive permutation groups.
متن کاملA general representation theory for constructing groups of permutation polynomials
Using the left regular action of a group on itself, we develop a general representation theory for constructing groups of permutation polynomials. As an application of the method, we compute polynomial representations of several abelian and nonabelian groups, and we determine the equivalence classes of the groups of polynomials we construct. In particular, when the size of the group is equal to...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Designs, Codes and Cryptography
سال: 2017
ISSN: 0925-1022,1573-7586
DOI: 10.1007/s10623-017-0381-1