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


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



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


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.


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.




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.

Most read articles by the same author(s)