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.
Karamanoglu Mehmetbey University
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
2015; 52(6): 2011-2023
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd