Subfield codes of CD-codes over F2[x]/⟨x3 - x⟩

A non-zero F-linear map from a finite-dimensional commutative F-algebra to the field Fis called an F-valued trace if its kernel does not contain any non-zero ideals. In this article, we utilize an F2-valued trace of the F2-algebra R2:= F2[x]/x3- x to study binary subfield code C(2) Dof CD:={(x center dot d) d.D: x. Rm2} for each defining set Dderived from a certain simplicial complex. For m. Nand X.{1, 2,..., m}, define X:={v. Fm2: Supp(v). X} and D :=(1 + u2) D1+ u2D2+(u + u2)D3, a subset of Rm2, where u = x + x3- x, D1.{L, cL}, D2.{ M, cM} and D3.{N, cN}, for L, M, N.{1, 2,..., m}. The parameters and the Hamming weight distribution of the binary subfield code C(2)Dof CDare determined for each D. These binary subfield codes are minimal under certain mild conditions on the cardinalities of L, Mand N. Moreover, most of these codes are distanceoptimal. Consequently, we obtain a few infinite families of minimal, self-orthogonal and distance-optimal binary linear codes that are either 2-weight or 4-weight. It is worth mentioning that we have obtained several new distance-optimal binary linear codes. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.