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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.
Alahmadi et al. (Fri,) studied this question.