On Linear Complementary-Dual Multinegacirculant Codes

Talk by Dr. Buket Özkaya

Speaker invited by: Prof. Dr. Joachim Rosenthal

Date: 29.03.17  Time: 15.00 - 16.00  Room: Y27H28

Linear complementary dual codes (LCD) are linear codes that intersect with their dual trivially. They were introduced by Massey, and rediscovered a few years ago in the context of sidechannel attacks. In a recent paper the class of quasi-cyclic LCD codes was shown to be “good”. The main result of the present paper is to show that some classes of one-generator quasitwisted codes, an odd characteristic analogue of quasi-cyclic codes, are not only good, but better than the Varshamov-Gilbert bound. Analogous techniques were used to characterize and enumerate self-dual double negacirculant codes, which also have infinite families with relative distance satisfying a modified Varshamov-Gilbert bound. In this work, multinegacirculant codes of index 2 that are LCD are characterized algebraically and some exact enumeration results for index 2 and index 3 are also derived by using their concatenated structure. For a general index t and co-index power of 2, a special enumeration is given which is needed for the asymptotic analysis by means of Dickson polynomials. A construction technique for index 2 (double negacirculant codes), and some examples of optimal or best such codes in modest lengths are given. The main technical ingredients of the proofs are some results on the number of solutions of certain diagonal equations over finite fields.