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,
Patrick Solé
Affiliations
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
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, Ep=a,b|pa=pb=0,a2=a,b2=b,ab=a,ba=b, where a≠b and p is any odd prime. We also give a classification of self-orthogonal codes and self-dual codes over Ep, where p=3,5, and 7, in short lengths.
