The Mass Formula for Self-Orthogonal and Self-Dual Codes over a Non-Unitary Non-Commutative Ring

Adel Alahmadi (), Altaf Alshuhail, Rowena Alma Betty, Lucky Galvez and Patrick Solé
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Adel Alahmadi: Research Group of Algebraic Structures and Applications, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Altaf Alshuhail: Research Group of Algebraic Structures and Applications, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Rowena Alma Betty: Institute of Mathematics, University of the Philippines-Diliman, Quezon City 1101, Philippines
Lucky Galvez: Institute of Mathematics, University of the Philippines-Diliman, Quezon City 1101, Philippines
Patrick Solé: I2M, (CNRS, University of Aix-Marseille, Centrale Marseille), 13009 Marseilles, France

Mathematics, 2024, vol. 12, issue 6, 1-11

Abstract: In this paper, we derive a mass formula for the self-orthogonal codes and self-dual codes over a non-commutative non-unitary ring, namely, E p = a , b | p a = p b = 0 , a 2 = a , b 2 = b , a b = a , b a = b , where a ≠ b and p is any odd prime. We also give a classification of self-orthogonal codes and self-dual codes over E p , where p = 3 , 5 , and 7, in short lengths.

Keywords: non-unitary non-commutative rings; left self-dual codes; self-dual codes; mass formula (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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