Some New Constructions of AFER-Optimal Binary Linear Block Codes
Murad Abdullah, Wai Ho Mow · 2023
In this paper, we present new constructions for binary linear block codes (BLBCs) that achieve the largest possible minimum Hamming weight and the smallest possible number of minimum-weight codewords (also known as the error coefficient). These [n, k] BLBCs over the additive white Gaussian noise channel, under maximum-likelihood decoding, attain the best possible asymptotic frame error rate (FER) (i.e., at high signal-to-noise ratio) and are said to be asymptotic frame error rate (AFER)-optimal. For l = 0, 1,⋯, k−1 and all positive integers k and m, we give new constructions of [(2k−1)m+l, k] and [12], [5] AFER-optimal codes. Specifically, we have [(2k− 1) + k, k + 1], [15m + 6, 4], and [15m + 4, 4] BLBCs with error coefficient values of 2, 3 and 4, respectively. These values are significantly smaller than the corresponding best-known values in the literature.