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

Creative Commons License

Karakaş B. E.

The 16th International Conference on Finite Fields and their Applications, Sao-Carlos, Brazil, 7 - 11 July 2025, pp.17, (Summary Text)

  • Publication Type: Conference Paper / Summary Text
  • City: Sao-Carlos
  • Country: Brazil
  • Page Numbers: pp.17
  • Middle East Technical University Affiliated: Yes

Abstract

Private Information Retrieval (PIR) scheme aims to retrieve data from a database without revealing any details about the identity of the retrieved data. The PIR scheme for coded storage systems with colluding servers gives a better PIR rate when a storage code and retrieval code have transitive automorphism groups. First, [2] used Reed-Muller codes as transitive codes. Then, [1] used cyclic codes as another family of transitive codes, and they showed that cyclic codes outperform Reed-Muller codes in terms of the PIR rate and the number of colluding servers. In this work, we study the transitivity of nD-cyclic codes and then PIR schemes from them together with several examples of nD-cyclic codes with better PIR rates. Then, we show the monomial equivalence between nD-cyclic codes and certain nD-constacyclic codes, which can be used as an alternative family of transitive codes.

References

[1] Ş. Bodur, E. Martinez-Moro, and D. Ruano, Private information retrieval schemes using cyclic codes, International Workshop on the Arithmetic of Finite Fields, Springer (2022), 194–207.

[2] R. Freij-Hollanti, O. W. Gnilke, C. Hollanti, A.-L. Horlemann-Trautmann, D. Karpuk, and I. Kubjas, t-private information retrieval schemes using transitive codes, IEEE Transactions on Information Theory 65 (2018), No. 4, 2107–2118.