A class of cyclic Codes Over the Ring $\Z_4[u]/<u^2>$ and its Gray image
Sukhamoy Pattanayak, Abhay Kumar Singh
TL;DR
This paper investigates cyclic codes over a specific ring and their binary images, revealing algebraic structures that enable the construction of good binary codes of length 28.
Contribution
It introduces a detailed study of cyclic codes over the ring ourour[u]/<u^2> and identifies new binary codes with desirable properties.
Findings
Identified algebraic structures of cyclic codes over the ring.
Constructed good ourour codes of length 28.
Demonstrated the binary images have promising error-correcting capabilities.
Abstract
Cyclic codes over R have been introduced recently. In this paper, we study the cyclic codes over R and their image. Making use of algebraic structure, we find the some good codes of length 28.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Cellular Automata and Applications