# Orthogonality and Conjugation for the Idempotents of Constacyclic Codes

A.J. van Zanten

Research output: Book/ReportReportProfessional

### 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 language English Tilburg University 45 Published - Sep 2016 Yes

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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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T1 - Orthogonality and Conjugation for the Idempotents of Constacyclic Codes

AU - van Zanten, A.J.

PY - 2016/9

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N2 - 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).

AB - 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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BT - Orthogonality and Conjugation for the Idempotents of Constacyclic Codes

PB - Tilburg University

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