Glift codes over chain ring and non-chain ring Re,s

Summary: 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 \(\mathcal{R}_{e,s}\).

Country

Turkey

Related Organizations

Karamanoğlu Mehmetbey University
Turkey

Keywords

optimal codes, distance preserving, Optimal Codes, zero divisor classification, Lifted Mds Codes, Distance Preserving, Other types of codes, lifted matrices, lifted polynomials, Bounds on codes, Glift Codes, Zero Divisor Classification, lifted MDS codes, Lifted Polynomials, glift codes, Lifted Matrices, Linear codes (general theory)

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