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Technical Program

Paper Detail

Paper IDD1-S7-T2.2
Paper Title Extended Cyclic Codes Sandwiched Between Reed-Muller Codes
Authors Changjiang Ji, Yan Xu, Sihuang Hu, Shandong University, China
Session D1-S7-T2: Algebraic Codes
Chaired Session: Tuesday, 13 July, 00:00 - 00:20
Engagement Session: Tuesday, 13 July, 00:20 - 00:40
Abstract The famous Barnes-Wall lattices can be obtained by applying Construction D to a chain of Reed-Muller codes. By applying Construction $D^{(cyc)}$ to a chain of extended cyclic codes sandwiched between Reed-Muller codes, Hu and Nebe (J. London Math. Soc. (2) 101 (2020) 1068-1089) constructed new series of universally strongly perfect lattices sandwiched between Barnes-Wall lattices. In this paper, we explicitly determine the minimum weight codewords of those codes for some special cases.