Construction of Linear Codes over Rings Zm Correcting Double ±1 or ±2 Errors

Authors

  • Gurgen H. Khachatrian American University of Armenia
  • Hamlet K. Khachatrian Institute for Informatics and Automation Problems of NAS RA

DOI:

https://doi.org/10.51408/1963-0008

Keywords:

Error correcting codes, Errors with magnitude ±1 and ±2

Abstract

In this paper a construction of double ±1 and ±2 errors correcting linear optimal and quasi-optimal codes over rings Z5, Z7 and Z9 is presented with the limitation that both errors have the same amplitude in absolute value.

References

S. Martirossian, “Single error correcting close packed and perfect codes”, Proc.1st INTAS Int. Seminar Coding Theory and combinatorics, Armenia, pp. 90-115, 1996.

H. Kostadinov, N. Manev and H. Morita, “On ±1 error correctable codes”, IEICE Trans.Fundamentals, vol. E93-A, pp. 2578-2761, 2010.

A. J. Han Vinck and H. Morita, “Codes over the ring of integers modulo m”, IEICE Trans.Fundamentals, vol. E81-A, pp. 2013-2018, 1998.

G. Khachatrian and H. Morita, “Construction of optimal ±1 double error correcting linear codes over ring Z5”, 3th International Workshop on Advances in Communications, Boppard, Germany, pp. 10-12, May 2014.

G. Khachatrian and H. Khachatrian ”Construction of double ±1 error correcting linear optimal codes over rings Z7 and Z9” Mathematical Problems of Computer Science, vol. 45, pp. 106--110, 2016.

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Published

2021-12-10

How to Cite

Khachatrian, G. H., & Khachatrian, H. K. (2021). Construction of Linear Codes over Rings Zm Correcting Double ±1 or ±2 Errors. Mathematical Problems of Computer Science, 49, 66–73. https://doi.org/10.51408/1963-0008

Issue

Vol. 49 (2018): Mathematical Problems of Computer Science

Section

Articles

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Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

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