Constructions of Quasi-Twisted Two-Weight Codes
Eric Z. Chen
TL;DR
This paper introduces a new method for constructing quasi-twisted two-weight codes from constacyclic codes, resulting in many new codes and expanding the understanding of their structure and applications.
Contribution
It presents a novel construction technique for QT two-weight codes based on constacyclic codes of composite length, leading to numerous new code examples.
Findings
Many new QT two-weight codes were discovered.
A transformation from constacyclic to quasi-twisted form was established.
Several new codes with desirable properties were constructed.
Abstract
A code is said to be two-weight if the non-zero codewords have only two different a weight w1 and w2. Two-weight codes are closely related to strongly regular graphs. In this paper. It is shown that a consta-cyclic code of composite length can be put in the quasi-twisted form. Based on this transformation, a new construction method of quasi-twisted (QT) two-weight codes is presented. A large amount of QT two-weight codes are found, and some new codes are also constructed.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Cellular Automata and Applications