Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2022; 59(6): 1557-1565

Online first article September 6, 2022      Printed November 30, 2022

https://doi.org/10.4134/BKMS.b210891

Copyright © The Korean Mathematical Society.

Glift codes over chain ring and non-chain ring $R_{e,s}$

Elif Segah Oztas

Karamanoglu Mehmetbey University

Abstract

In this paper, Glift codes, generalized lifted polynomials, matrices are introduced. The advantage of Glift code is ``distance preserving" over the ring $\mathcal{R}$. Then optimal codes can be obtained over the rings by using Glift codes and lifted polynomials. Zero divisors are classified to satisfy ``distance preserving" for codes over non-chain rings. Moreover, Glift codes apply on MDS codes and MDS codes are obtained over the ring $\mathcal{R}$ and the non-chain ring $\mathcal{R}_{e,s}$.

Keywords: Glift codes, lifted polynomials, lifted matrices, optimal codes, lifted MDS codes, distance preserving, zero divisor classification

MSC numbers: Primary 94B05, 94B60, 94B65

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