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# Higher-order CIS codes

## 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 Yes Dual distance; Boolean functions; Z4-linear codes; quasi-cyclic codes Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics IIFacultiesFaculties > Faculty of Mathematics, Physics und Computer ScienceFaculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Yes 500 Science > 510 Mathematics 19 Nov 2014 10:19 04 Feb 2015 09:00 https://eref.uni-bayreuth.de/id/eprint/3644