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Hamming codes are of primary concern in information theory and its applications. Despite a number of researches that have been conducted on such codes and their characterizations, dealing with the properties of previously introduced codes in a BCK-algebraic framework has not been considered in earlier works. This paper investigates a code constructed based on BCK-algebraic models and proposes an algorithm corresponding to the presented code. It is noticeable that the suggested rendered algorithm is also established on the basis of the elements of a BCK-algebra. In fact, both the Hamming distance and dimension, associated with the presented code, can be estimated through a BCK-algebra structure due to the mechanism of its algorithm which is heavily dependent on the parity check matrix. In addition, the way in which the codes are designed contributes substantially to classification of them and to extract greater number of their attributes compared to the previous works. The highlight of the proposed method is that the number of atoms of the BCK-algebra plays a key role in calculation of the Hamming distance and dimension of these codes. Moreover, the obtained codes possess specified and recognizable Hamming distance which are essential in performing error-correcting, error-detecting and decoding tasks. [ABSTRACT FROM AUTHOR]

The idea of the inverse optimization problem is to adjust the value of the parameters such that the observed feasible solution becomes optimal. The modification cost can be measured by different norms, such as l 1 , l 2 , l ∞ norms and the Hamming distance, and the goal is to adjust the parameters as little as possible. In this paper, we consider the inverse minimum flow problem under the weighted sum-type Hamming distance, where the lower and upper bounds for the arcs should be changed as little as possible under the weighted sum-type Hamming distance such that a given feasible flow becomes a minimum flow. Two models are considered: the unbounded case and the general bounded case. We present their respective combinatorial algorithms that both run in O ( n m ) time in terms of the minimum cut method. Computational examples are presented to illustrate our algorithms. [ABSTRACT FROM AUTHOR]

Motif finding is an important and a challenging problem in many biological applications such as discovering promoters, enhancers, locus control regions, transcription factors, and more. The ( l, d)-planted motif search, PMS, is one of several variations of the problem. In this problem, there are n given sequences over alphabets of size , each of length m, and two given integers l and d. The problem is to find a motif m of length l, where in each sequence there is at least an l-mer at a Hamming distance of of m. In this article, we propose ET-Motif, an algorithm that can solve the PMS problem in time and space. The time bound can be further reduced by a factor of m with space. In case the suffix tree that is built for the input sequences is balanced, the problem can be solved in time and space. Similarly, the time bound can be reduced by a factor of m using space. Moreover, the variations of the problem, namely the edit distance PMS and edited PMS (Quorum), can be solved using ET-Motif with simple modifications but upper bands of space and time. For edit distance PMS, the time and space bounds will be increased by , while for edited PMS the increase will be of in the time bound. [ABSTRACT FROM AUTHOR]

The most common iris biometric algorithm represents the texture of an iris using a binary iris code. Not all bits in an iris code are equally consistent. A bit is deemed fragile if its value changes across iris codes created from different images of the same iris. Previous research has shown that iris recognition performance can be improved by masking these fragile bits. Rather than ignoring fragile bits completely, we consider what beneficial information can be obtained from the fragile bits. We find that the locations of fragile bits tend to be consistent across different iris codes of the same eye. We present a metric, called the fragile bit distance, which quantitatively measures the coincidence of the fragile bit patterns in two iris codes. We find that score fusion of fragile bit distance and Hamming distance works better for recognition than Hamming distance alone. To our knowledge, this is the first and only work to use the coincidence of fragile bit locations to improve the accuracy of matches. [ABSTRACT FROM PUBLISHER]

Previous interleavers designed for Serially Concatenated Codes (SCCs) have achieved a limited Minimum Hamming Distance (MHD) between the legitimate permutations of the encoded bit sequence. Hence, we propose a novel Evolutionary Algorithm (EA) capable of designing improved interleavers for SCCs, without artificially limiting the achievable MHD. As a result, increased MHDs and therefore reduced error floors are achieved, even if only a modest EA complexity can be afforded. [ABSTRACT FROM PUBLISHER]