Nettet1. des. 2024 · Linear codes over finite rings also have a lot of outstanding and remarkable applications, and have been studied since Hammons et al. found significant classes of Z 4 -codes such as the Kerdock, Preparata, Goethals codes and so on [11]. For more details of codes over finite rings, see [23]. Nettet24. mar. 2024 · A linear code over a finite field with q elements F_q is a linear subspace C subset F_q^n. The vectors forming the subspace are called codewords. When …

(PDF) Skew cyclic Linear codes over 𝑹 = 𝑅 + 𝑤𝑅 + 𝑤2𝑅

Nettet2.2. Codes over chain rings A linear code Cof length nover the ring Ris defined to be a submodule of the R-module Rn. We will denote by f0g, the zero-submodule where 0 = (0;0;:::;0) 2Rn. A linear code Cover Ris free if C˘=Rkas R-modules for some positive integer k. The residue code of a linear code Cover Ris the linear code ˇ(C) over F q ˇ ... NettetA linear code C over the ring ℤ 15 is a additive sub-module. For every code word x = ( x 1, x 2, ⋯, x n) and y = ( y 1, y 2, ⋯, y n) in C, the inner product of x and y is defined as 〈 … jefferson indiana assesor

On the Construction of Quantum and LCD Codes from Cyclic Codes over …

NettetWe introduce a new type of linear and cyclic codes. These codes are defined over a direct product of 2 finite chain rings. The definition of these codes as certain … http://maths.ccnu.edu.cn/info/1045/28050.htm NettetThe aim of this paper is to develop a theory of linear codes over nite chain rings from a geometric viewpoint. Generalizing a well-known result for lin-ear codes over elds, we … jefferson indiana jail