GENERATORS IDEMPOTENT IN SEMI-SIMPLE RING $FC_{16p^n}$, FOR THE IDEALS CORRESPONDING TO THE MINIMAL CYCLIC CODES OF LENGTH $16p^n$ AND THE CODES

Print ISSN: 0972-7752 | Online ISSN: 2582-0850

Abstract

In semi-simple ring $R_{16p^n}\equiv \frac{GF(q)[x]}{<x^{16p^n}-1>}$, where $p$ is prime and $q$ is some prime power (of type $16k+1$), $n$ is a positive integer, subject to order of $q$ modulo $p^n$ is $\frac{\phi(p^n)}{2}$, expression for primitive idempotents are obtained. Generating polynomials, dimensions and minimum distance bounds for the cyclic codes generated by these idempotents are also calculated.

Keywords and Phrases

Cyclotomic cosets, primitive idempotents, generating polynomials, minimum distance.

A.M.S. subject classification

11T71, 11T55, 22D20.

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