PIR Schemes from nD-Cyclic and nD-Constacyclic Codes and Their Monomial Equivalence

Abstract Private Information Retrieval (PIR) scheme aims to retrieve data from a database without revealing any details about the identity of the data. The PIR scheme for coded storage systems with colluding servers gives a better PIR rate when the storage code and retrieval code have transitive automorphism groups. In this work, we study the transitivity of n D-cyclic codes and then PIR schemes from them together with several examples of n D-cyclic codes with better PIR rates. Then, we show the monomial equivalence between n D-cyclic codes and certain n D-constacyclic codes, which can be used as an alternative family of transitive codes.