Linear Complementary Dual codes (LCD) are binary linear codes that meet their dual trivially. These codes were introduced by Massey in [4] from an Information Theory standpoint; they give an optimum linear coding solution for the two user binary adder channel. They were rediscovered recently in the context of counter measures to passive and active side channel analyses on embedded cryto-systems, see [2] for a detailed description. In two recent
preprints the authors with some collaborators have studied such codes from a normative and constructive viewpoint; on one hand combinatorial upper bounds on the size of such codes of given error correcting capacity have been derived [1]; on the other hand algebraic constructions of the quasi-cyclic (QC) subclass have been given [3].

In the proposed meeting the authors propose to pursue the exploration of LCD codes in the following directions. For QC LCD codes the problem of exact enumeration which could lead to improve asymptotics and can use enumeration of all LCD codes is still open. Another constructive approach is to use AG codes over large alphabets, a domain in which CG and FO have a great deal of experience to construct explicit in nite families of long LCD codes by concatenation.

[1] Steven T. Dougherty, Jon-Lark Kim, Buket Ozkaya, Lin Sok, Patrick Sol, The
combinatorics of LCD codes: linear programming bound and orthogonal matrices, http://arxiv.org/abs/1506.01955
[2] C. Carlet and S. Guilley, \Complementary dual codes for counter-measures to sidechannel
attacks », Proceedings of the 4th ICMCTA Meeting, Palmela, Portugal, 2014.
[3] C. Gueneri, B. Ozkaya, P. Sole, Quasi-Cyclic Complementary Dual Code,
http://arxiv.org/abs/1506.01971
[4] J.L. Massey, Linear codes with complementary duals, Discrete Mathematics, 106 – 107,
337-342, 1992.

Participants

Claude Carlet (Universités Paris 8 et Paris 13)
Cem Güneri (Sabanci University, Turkey)
Ferruh Ozbudak (Middle East Technical University, Turkey)
Patrick Solé (Institut Mines-Télécom, Paris)