Speaker: 陈豪教授，暨南大学

Title: Linear Codes from Projective Linear Anticodes Revisited

Language: Chinese

Time & Venue: 2024.06.22 10:40-11:40 思源楼515

Abstract: In this talk, we give an antiGriesmer bound for q-ary projective linear anticodes, which is stronger than the above Erd ̈os-Kleitman bound for binary anticodes. The antiGriesmer bound is a lower bound on diameters of projective linear anticodes. From some known projective linear anticodes, we construct some linear codes with optimal or near optimal minimum distances. A complementary theorem constructing infinitely many new projective linear (t+1)-weight code from a known t-weight linear code is presented. Then many new optimal or almost optimal few-weight linear codes are given and their weight distributions are determined. As a by-product, we also construct several infinite families of three-weight binary linear codes, which lead to l-strongly regular graphs for each odd integer l ≥ 3.