Iso-Orthogonality and Type II Duadic Constacyclic Codes
Yun Fan, Liang Zhang
TL;DR
This paper introduces and studies even-like (Type-II) duadic constacyclic codes, establishing their orthogonality, duality properties, and existence conditions, and constructs a class of MDS codes within this framework.
Contribution
It generalizes duadic cyclic and negacyclic codes to constacyclic codes, providing new existence criteria and explicit constructions including MDS codes.
Findings
Even-like duadic constacyclic codes are isometrically orthogonal.
Duals of even-like codes are odd-like duadic constacyclic codes.
Necessary and sufficient conditions for existence of even-like duadic codes.
Abstract
Generalizing even-like duadic cyclic codes and Type-II duadic negacyclic codes, we introduce even-like (i.e.,Type-II) and odd-like duadic constacyclic codes, and study their properties and existence. We show that even-like duadic constacyclic codes are isometrically orthogonal, and the duals of even-like duadic constacyclic codes are odd-like duadic constacyclic codes. We exhibit necessary and sufficient conditions for the existence of even-like duadic constacyclic codes. A class of even-like duadic constacyclic codes which are alternant MDS-codes is constructed.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Cryptographic Implementations and Security