A new test called rotation search is proposed for user identification and cryptographic key regeneration in systems employing a digital representation of the iris which is called the iris code. When applied to the BIOSECURE, CASIA and NIST-ICE data bases the rotation search shows, on average, a two fold reduction in false rejection ratio (FRR) with a false acceptance ratio (FAR) equal to zero, in comparison with the standard search employed in other systems. The highest improvement reached in FRR by the rotation search against the standard search is about 100 times for a single iris and 85 times for the two irides of a user, and in many cases the measured FRR is equal to zero. . Prof. da Rocha research interests are in applied digital information theory, including error-correcting codes and cryptography. He has published over 100 engineering and scientific papers, including journal and conference papers, and the books Communication Systems, Springer, 2005, and Elements of Algebraic Coding Systems, Momentum Press, 2014. He is currently a Member of the IEEE Alexander Graham Bell Medal Committee.

A condition is proven on the roots of the generator polynomial of a q-ary cyclic code of block length n which guarantees full cyclic order for all nonzero codewords. For such cyclic codes having n = q m − 1, a theorem is proven which allows to partition the set of all nonzero codewords into cyclic equivalence classes of order n.Introduction: In this Letter, a condition is proven on the roots of the generator polynomial of a linear q-ary cyclic code C of block length n which guarantees full cyclic order for all nonzero codewords, where q is the power of a prime and n is a positive integer which divides q m − 1. For such cyclic codes having n = q m − 1, a theorem is proven which allows a systematic partition of the set of all nonzero codewords of C into cyclic equivalence classes of order n [1]. We refer to this latter result as the separation theorem. The goal of the theory in this Letter is the construction of 'cyclically permutable codes' [2].Binary cyclically permutable codes have many applications as, for example, protocol sequences for the collision channel without feedback [1,3], as well as improving robustness against clipping attacks of watermarking systems [4]. Additionally, non-binary cyclically permutable codes have applications in direct sequence code division multiple access (DS-CDMA) systems with asynchronous base stations [5].In [1], conditions are given that should be obeyed by a construction of a cyclically permutable code. The first condition is that the technique for specifying equivalence classes must be easy to build. The second condition specifies the efficiency of the construction, namely, for a given a q-ary cyclic code with block length n, having q k codewords, the number of distinct cyclic equivalence classes produced should be close to the maximum value of q k /n. A third desirable condition is that the minimum Hamming distance of the cyclically permutable code should approach the maximum possible value for the given code parameters. In the sequel, we show that the proposed approach for generating cyclically permutable codes is easily implementable, and for linear q-ary cyclic codes it is optimal in the sense that the number of cyclic equivalence classes selected is precisely (q k − 1)/n, obtained by removing the allzero codewords because it has cyclic order 1 (see Definition 1).

No abstract

Uniform constant composition (UCC) codes are introduced, which are p-ary constant composition codes with block length mp where each p-ary symbol appears exactly m times in each codeword, being m a positive integer and p a prime. UCC codes are derived from a new class of p-ary repeated-root cyclic codes and two constructions are presented. Both constructions are at least asymptotically optimal with increasing p when compared with known best bounds for constant composition codes. Introduction: A constant composition code [1] is a block code defined over an alphabet with q symbols, denoted as 1, 2,. .. , q, the codebook of which consists of codewords where the symbol i occurs w i times, 1 ≤ i ≤ q, and is usually a non-linear code. We define a uniform constant composition (UCC) code as a constant composition code of block length mq, where m is a positive integer, for which w i = m, 1 ≤ i ≤ q. In this Letter, we consider only p-ary UCC codes of block length mp, where p is a prime, m is a positive integer, m ò 0 mod p, i.e. m is not a multiple of p, since the codes resulting when m ; 0 mod p represent a straightforward generalisation. Constant composition codes have recently been considered for important applications requiring non-binary alphabets [2] as, for example, power-line communications [3], construction of DNA codes [4], multiple-access communications and frequency hopping [5]. In order to construct UCC codes, we first introduce a class of p-ary (n, k, d) repeated-root cyclic codes with block length n = mp, k information symbols and minimum distance d. Two code constructions are presented, each one characterised by the corresponding p-ary generator polynomial g(x), which is a factor of x n − 1, with the remark that n = mp is the smallest value of n for which g(x) divides x n − 1. Construction 1 produces (mp, 2, m(p − 1)) codes which have a subset of M 1 = p(p − 1) UCC codewords, while Construction 2 produces (mp, m + 1, d) codes, with d = p − 1 for m = 1 and d = p for m ≥ 2, which have a subset of M 2 = p m (p − 1) UCC codewords.

A cyclically permutable code is a binary code the codewords of which are cyclically distinct and have full cyclic order. The purpose of this paper is to construct cyclically permutable codes by means of linear p-ary constacyclic codes, where p denotes a prime number. An efficient method is used to select codewords from a constacyclic code which are constacyclically distinct and have full constacyclic order. Through a cyclic representation for the elements of GF(p) and by a correspondence of two-dimensional arrays and N-tuples, the codewords selected produce the codebook of a cyclically permutable code. The cyclically permutable codes constructed are used in the construction of protocol sequences for the Mactive-out-of-T users collision channel without feedback.