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Optical orthogonal signature pattern codes (OOSPCs) have played an important role in a novel type of optical code-division multiple-access network for 2-D image transmission. In this paper, we give four direct constructions for OOSPCs based on polynomials and rational functions over finite fields. We also use $r$ -simple matrices to present a recursive construction for OOSPCs. These constructions yield new families of asymptotically optimal OOSPCs. [ABSTRACT FROM AUTHOR]

Frequency hopping sequences (FHSs) are employed to mitigate the interferences caused by the hits of frequencies in frequency hopping spread spectrum systems. In this paper, we present combinatorial constructions for FHS sets, including direct constructions by using cyclotomic classes, recursive constructions based on cyclic difference matrices, merging blocks, and discrete logarithm. By these constructions, a number of series of new FHS sets are then produced. These FHS sets are optimal with respect to the Peng–Fan bounds. [ABSTRACT FROM PUBLISHER]

Frequency hopping sequences (FHSs) with favorable partial Hamming correlation properties have important applications in many synchronization and multiple-access systems. In this paper, we investigate constructions of FHSs and FHS sets with optimal partial Hamming correlation. We first establish a correspondence between FHS sets with optimal partial Hamming correlation and multiple partition-type balanced nested cyclic difference packings with a special property. By virtue of this correspondence, some FHSs and FHS sets with optimal partial Hamming correlation are constructed from various combinatorial structures, such as cyclic difference packings and cyclic relative difference families. As a consequence, our constructions yield new FHSs and FHS sets with optimal partial Hamming correlation. [ABSTRACT FROM AUTHOR]

We study (symbol-pair) codes for symbol-pair read channels introduced recently by Cassuto and Blaum (2010). A Singleton-type bound on symbol-pair codes is established and infinite families of optimal symbol-pair codes are constructed. These codes are maximum distance separable (MDS) in the sense that they meet the Singleton-type bound. In contrast to classical codes, where all known q-ary MDS codes have length O(q), we show that q-ary MDS symbol-pair codes can have length \Omega (q^2). In addition, we completely determine the existence of MDS symbol-pair codes for certain parameters. [ABSTRACT FROM AUTHOR]

Multimedia fingerprinting is an effective technique to trace the sources of pirate copies of copyrighted multimedia information. Separable codes can be used to construct fingerprints resistant to the averaging collusion attack on multimedia contents. In this paper, we investigate \overlinet-separable codes from a combinatorial point of view. We first derive several upper bounds on the sizes of \overlinet-separable codes, and then turn our attention to the constructions of optimal \overline2-separable codes with short length. Two infinite families of optimal \overline2-separable codes of length 2 are constructed from projective planes, and all optimal \overline2-separable codes of length 3 are explicitly constructed by means of difference matrices. These optimal \overline2-separable codes with short length can be used to construct good \overline2-separable codes with long length by a known composition construction. [ABSTRACT FROM AUTHOR]