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 | Total Downloads : 152
DOI:
Author :
Vishvajit Singh (Department of Mathematics, I.G. University, Meerpur, Rewari, INDIA)
Manju Pruthi (Department of Mathematics, Maharshi Dayanand University, Rohtak, INDIA)
Jagbir Singh (Department of Mathematics, Maharshi Dayanand University, Rohtak, INDIA)
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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