On regular and new types of codes for location-domination

Identifying codes and locating-dominating codes have been designed for locating irregularities in sensor networks. In both cases, we can locate only one irregularity and cannot even detect multiple ones. To overcome this issue, self-identifying codes have been introduced which can locate one irregularity and detect multiple ones. In this paper, we define two new classes of locating-dominating codes which have similar properties. These new locating-dominating codes as well as the regular ones are then more closely studied in the rook’s graphs and binary Hamming spaces.In the rook’s graphs, we present optimal codes, i.e., codes with the smallest possible cardinalities, for regular location-domination as well as for the two new classes. In the binary Hamming spaces, we present lower bounds and constructions for the new classes of codes; in some cases, the constructions are optimal. Moreover, one of the obtained lower bounds improves the bound of Honkala et al. (2004) on codes for locating multiple irregularities.Besides studying the new classes of codes, we also present record-breaking constructions for regular locating-dominating codes. In particular, we present a locating-dominating code in the binary Hamming space of length 11 with 320 vertices improving the earlier bound of 352; the best known lower bound for such code is 309 by Honkala et al. (2004).</p

Large Constant Dimension Codes and Lexicodes

Constant dimension codes, with a prescribed minimum distance, have found recently an application in network coding. All the codewords in such a code are subspaces of \F_q^n with a given dimension. A computer search for large constant dimension codes is usually inefficient since the search space domain is extremely large. Even so, we found that some constant dimension lexicodes are larger than other known codes. We show how to make the computer search more efficient. In this context we present a formula for the computation of the distance between two subspaces, not necessarily of the same dimension.Comment: submitted for ALCOMA1

Coding Theory and Algebraic Combinatorics

This chapter introduces and elaborates on the fruitful interplay of coding theory and algebraic combinatorics, with most of the focus on the interaction of codes with combinatorial designs, finite geometries, simple groups, sphere packings, kissing numbers, lattices, and association schemes. In particular, special interest is devoted to the relationship between codes and combinatorial designs. We describe and recapitulate important results in the development of the state of the art. In addition, we give illustrative examples and constructions, and highlight recent advances. Finally, we provide a collection of significant open problems and challenges concerning future research.Comment: 33 pages; handbook chapter, to appear in: "Selected Topics in Information and Coding Theory", ed. by I. Woungang et al., World Scientific, Singapore, 201

Satisfiability, sequence niches, and molecular codes in cellular signaling

Biological information processing as implemented by regulatory and signaling networks in living cells requires sufficient specificity of molecular interaction to distinguish signals from one another, but much of regulation and signaling involves somewhat fuzzy and promiscuous recognition of molecular sequences and structures, which can leave systems vulnerable to crosstalk. This paper examines a simple computational model of protein-protein interactions which reveals both a sharp onset of crosstalk and a fragmentation of the neutral network of viable solutions as more proteins compete for regions of sequence space, revealing intrinsic limits to reliable signaling in the face of promiscuity. These results suggest connections to both phase transitions in constraint satisfaction problems and coding theory bounds on the size of communication codes

Iris Codes Classification Using Discriminant and Witness Directions

The main topic discussed in this paper is how to use intelligence for biometric decision defuzzification. A neural training model is proposed and tested here as a possible solution for dealing with natural fuzzification that appears between the intra- and inter-class distribution of scores computed during iris recognition tests. It is shown here that the use of proposed neural network support leads to an improvement in the artificial perception of the separation between the intra- and inter-class score distributions by moving them away from each other.Comment: 6 pages, 5 figures, Proc. 5th IEEE Int. Symp. on Computational Intelligence and Intelligent Informatics (Floriana, Malta, September 15-17), ISBN: 978-1-4577-1861-8 (electronic), 978-1-4577-1860-1 (print