## Title data

Carlet, Claude ; Freibert, Finley ; Guilley, Sylvain ; Kiermaier, Michael ; Kim, Jon-Lark ; Solé, Patrick:

**Higher-order CIS codes.**

*In:* IEEE Transactions on Information Theory.
Vol. 60
(September 2014)
Issue 9
.
- pp. 5283-5295.

ISSN 0018-9448

DOI: https://doi.org/10.1109/TIT.2014.2332468

## Abstract in another language

We introduce complementary information set codes of higher order. A binary linear code of length tk and dimension k is called a complementary information set code of order t (t-CIS code for short) if it has t pairwise disjoint information sets. The duals of such codes permit to reduce the cost of masking cryptographic algorithms against side-channel attacks. As in the case of codes for error correction, given the length and the dimension of a t-CIS code, we look for the highest possible minimum distance. In this paper, this new class of codes is investigated. The existence of good long CIS codes of order 3 is derived by a counting argument. General constructions based on cyclic and quasi-cyclic codes and on the building up construction are given. A formula similar to a mass formula is given. A classification of 3-CIS codes of length ≤ 12 is given. Nonlinear codes better than linear codes are derived by taking binary images of Z4-codes. A general algorithm based on Edmonds’ basis packing algorithm from matroid theory is developed with the following property: given a binary linear code of rate 1/t, it either provides t disjoint information sets or proves that the code is not t-CIS. Using this algorithm, all optimal or best known [tk, k] codes, where t = 3, 4, …, 256 and 1 ≤ k ≤ ⌊256/t⌋ are shown to be t-CIS for all such k and t, except for t = 3 with k = 44 and t = 4 with k = 37.

## Further data

Item Type: | Article in a journal |
---|---|

Refereed: | Yes |

Keywords: | Dual distance; Boolean functions; Z4-linear codes; quasi-cyclic codes |

Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 19 Nov 2014 10:19 |

Last Modified: | 04 Feb 2015 09:00 |

URI: | https://eref.uni-bayreuth.de/id/eprint/3644 |