The classification of complementary information set codes of lengths 14 and 16

In the paper " A new class of codes for Boolean masking of cryptographic computations , " Carlet, Gaborit, Kim, and Solé defined a new class of rate one-half binary codes called complementary information set (or CIS) codes. The authors then classified all CIS codes of length less than or equal to 12. CIS codes have relations to classical Coding Theory as they are a generalization of self-dual codes. As stated in the paper, CIS codes also have important practical applications as they may improve the cost of masking cryptographic algorithms against side channel attacks. In this paper, we give a complete classification result for length 14 CIS codes using an equivalence relation on GL(n, F2). We also give a new classification for all binary [16, 8, 3] and [16, 8, 4] codes. We then complete the classification for length 16 CIS codes and give additional classifications for optimal CIS codes of lengths 20 and 26. A generalization of self-dual codes was recently proposed by Carlet, Gaborit, Kim, and Solé in [5]. In the paper, a new class of codes, called complementary information set (or CIS) codes, is defined. Given an integer n, a binary linear code with parameters [2n, n, d] which has two disjoint information sets is a complementary information set code. CIS codes have a variety of connections and applications; the authors (in [5]) note the direct applications found in Cryptography, with relations to Boolean S-Boxes, Boolean functions, and masking [13], [14], [15], [20]. Previous results on the classification of rate one-half codes date back to Pless' enumeration of self-dual codes in 1972 [18]. Since that time many classification results for self-dual codes have been obtained, most recently the doubly-even self-dual codes of length 40 [3]. A related problem is the classification of formally self-dual codes. The main results in this direction are classifications of optimal formally self-dual codes; results have been given in [1], [2], [7], [10]. Betsumiya and Harada gave a complete classification for even formally self-dual codes up to length 16 [2]; Han, H. Lee, and Y. Lee gave a complete classification for odd formally self-dual codes up to length 14 [10]. Some general results on optimal rate one-half codes were obtained by Gulliver and¨Ostergard in [9]. In the paper [5], CIS codes are classified for 2n = 2, 4, 6, 8, 10, 12. In the proceeding sections we obtain new results in the …