Grassl, Markus and Karakaş, Burcu Ecem and Özbudak, Ferruh and Özkaya, Buket (2026) PIR schemes from nD-Cyclic and nD-Constacyclic codes and their monomial equivalence. Computational and Applied Mathematics, 45 (6). ISSN 2238-3603 (Print) 1807-0302 (Online)
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Official URL: https://dx.doi.org/10.1007/s40314-026-03635-2
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 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.
| Item Type: | Article |
|---|---|
| Additional Information: | This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| Uncontrolled Keywords: | 68P20; 68P30; 94B15; 94B60; nD-constacyclic codes; nD-cyclic codes; Private information retrieval; Tansitive codes |
| Divisions: | Faculty of Engineering and Natural Sciences |
| Depositing User: | Ferruh Özbudak |
| Date Deposited: | 07 Apr 2026 10:27 |
| Last Modified: | 07 Apr 2026 10:27 |
| URI: | https://research.sabanciuniv.edu/id/eprint/53720 |
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