Negacyclotomic Cosets and Negacyclonomials of Negacyclic Codes

A.J. van Zanten

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Abstract

This report is a continuation of two previous reports dealing with so-called constacyclotomic cosets and constacyclonomials of constacyclic codes. These notions are studied more closely and applied to the special case of negacyclic case. A digraph is defined such that its leaves correspond to negacyclotomic cosets and its internal vertices to negacyclonomials. This graph appears to consist of the union of disconnected subtrees. It is proved that the number of negacyclotomic cosets is equal to the number of negacyclonomials in each subtree, and therefore also for the complete graph itself.
Original languageEnglish
PublisherTilburg University
Number of pages27
Publication statusPublished - 2015
Externally publishedYes

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van Zanten, A. J. (2015). Negacyclotomic Cosets and Negacyclonomials of Negacyclic Codes. Tilburg University.
van Zanten, A.J. / Negacyclotomic Cosets and Negacyclonomials of Negacyclic Codes. Tilburg University, 2015. 27 p.
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van Zanten, AJ 2015, Negacyclotomic Cosets and Negacyclonomials of Negacyclic Codes. Tilburg University.

Negacyclotomic Cosets and Negacyclonomials of Negacyclic Codes. / van Zanten, A.J.

Tilburg University, 2015. 27 p.

Research output: Book/ReportReportProfessional

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AB - This report is a continuation of two previous reports dealing with so-called constacyclotomic cosets and constacyclonomials of constacyclic codes. These notions are studied more closely and applied to the special case of negacyclic case. A digraph is defined such that its leaves correspond to negacyclotomic cosets and its internal vertices to negacyclonomials. This graph appears to consist of the union of disconnected subtrees. It is proved that the number of negacyclotomic cosets is equal to the number of negacyclonomials in each subtree, and therefore also for the complete graph itself.

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van Zanten AJ. Negacyclotomic Cosets and Negacyclonomials of Negacyclic Codes. Tilburg University, 2015. 27 p.