Optimal binary constant weight codes and affine linear groups over finite fields

作     者：Hou, Xiang-Dong 

作者机构：Univ S Florida Dept Math & Stat Tampa FL 33620 USA 

出 版 物：《DESIGNS CODES AND CRYPTOGRAPHY》 (设计、编码与密码学)

年 卷 期：2019年第87卷第8期

页      面：1815-1838页

核心收录：

学科分类：07[理学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 070101[理学-基础数学] 

主　　题：Affine linear group BIBD Constant weight code Johnson bound 

摘      要：The affine linear group of degree one, AGL(1,Fq), over the finite field Fq, acts sharply two-transitively on Fq. Given SAGL(1,Fq) and an integer k, 1kq, does there exist a k-element subset B of Fq whose set-wise stabilizer is S? Our main result is the derivation of two formulas which provide an answer to this question. This result allows us to determine all possible parameters of binary constant weight codes that are constructed from the action of AGL(1,Fq) on Fq to meet the Johnson bound. Consequently, for many parameters, we are able to determine the values of the function A2(n,d,w), which is the maximum number of codewords in a binary constant weight code of length n, weight w and minimum distance d.