A note on checkable codes over Frobenius and quasi-Frobenius rings

Abstract

We study checkable codes in finite Frobenius and quasi-Frobenius rings and show that the Jacobson radical of a quasi-Frobenius ring is checkable if and only if the ring is Frobenius. Also, we show that in a quasi-Frobenius ring R R every maximal left ideal is checkable and that R R is code-checkable if and only if R R is a principal right ideal ring.