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چکیده
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In this thesis, we study the structure of quadratic residue codes over the ring R = Fpr + u1Fpr + u2Fpr + ::: + utFpr and survey known results on quadratic residue codes over the field Fpr and give general properties with quadratic residue codes over R. Moreover, we introduce the Gray map from R to Ft+1 pr and obtain a number of Hermitian self-dual codes over R. Finally, we present a method to construct quantum codes over Fpr from quadratic residue codes over the ring R = Fpr +vFpr and obtain a number of quantum codes. Some of these quantum codes are MDS.
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