报告人：常彦勋教授（北京交通大学）
报告时间：2022年4月13日(周三)上午10：30-11：30
腾讯会议：329-756-437
报告摘要： An (n, d, {w1, w2})q code is a q-ary code of length n and Hamming distance at least d, which have two weights w1 and w2. Let Aq(n, d, {w1, w2}) denote the largest possible number of codewords in an (n, d, { w1, w2})q code and we simply write A(n, d, { w1, w2}) for A2(n, d, { w1, w2}). Some upper bounds on Aq(n, d, { w1, w2}) are given. The equivalences between binary two-weight codes and special combinatorial configurations with certain properties are established and then new upper bounds on A(n, d, {w1, w2}) are derived. For w1, w2 ∈{2, 3, 4}, optimal constructions of (n, d, { w1, w2})2 codes are presented. The exact value of A(n, d, {2, 3}) is completely determined for all n and d. We determine the exact value of A(n, d, {2, 4}) for any positive integer n ≡ 2, 4 (mod 6) and d ∈ {3, 4}. The exact value of A(n, d, {3, 4}) is determined for any integer n and d ∈ {6, 7}, or d = 5 and n ≡ 0, 2, 3, 11 (mod 12).
邀请人:季利均