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<p>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 <i>n</i>D-cyclic codes and then PIR schemes from them together with several examples of <i>n</i>D-cyclic codes with better PIR rates. Then, we show the monomial equivalence between <i>n</i>D-cyclic codes and certain <i>n</i>D-constacyclic codes, which can be used as an alternative family of transitive codes.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月3日

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  • Markus Grassl,
  • Burcu Ecem Karakaş,
  • Ferruh Özbudak,
  • Buket Özkaya

摘要

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 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.