Orthogonality and Conjugation for the Idempotents of Constacyclic Codes

A.J. van Zanten

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Abstract

The orthogonality relations for the idempotent generators for constacyclic codes are studied. It turns out that these relations give rise to a square table for these idempotents such that the rows are indexed by constacyclonomials and the columns by generating irreducible polynomials (or constacyclotomic cosets), and such that there is orthogonality, by using weight factors, between rows as well as between columns. This phenomenon resembles the properties of the character table of a finite group. This resemblance is strengthened by the existence of conjugated constacyclonomials and conjugated irreducible polynomials (or conjugated constacyclotomic cosets).
Original languageEnglish
PublisherTilburg University
Number of pages45
Publication statusPublished - Sep 2016
Externally publishedYes

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Irreducible polynomial
Coset
Conjugation
Orthogonality
Idempotent
Character Table
Orthogonality Relations
Table
Finite Group
Generator

Cite this

van Zanten, A.J. / Orthogonality and Conjugation for the Idempotents of Constacyclic Codes. Tilburg University, 2016. 45 p.
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abstract = "The orthogonality relations for the idempotent generators for constacyclic codes are studied. It turns out that these relations give rise to a square table for these idempotents such that the rows are indexed by constacyclonomials and the columns by generating irreducible polynomials (or constacyclotomic cosets), and such that there is orthogonality, by using weight factors, between rows as well as between columns. This phenomenon resembles the properties of the character table of a finite group. This resemblance is strengthened by the existence of conjugated constacyclonomials and conjugated irreducible polynomials (or conjugated constacyclotomic cosets).",
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Orthogonality and Conjugation for the Idempotents of Constacyclic Codes. / van Zanten, A.J.

Tilburg University, 2016. 45 p.

Research output: Book/ReportReportProfessional

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van Zanten AJ. Orthogonality and Conjugation for the Idempotents of Constacyclic Codes. Tilburg University, 2016. 45 p.