In this paper we use the Gray code representation of the genetic code C=00, U=10, G=11 and A=01 (C pairs with G, A pairs with U) to generate a sequence of genetic code-based matrices. In connection with these code-based matrices, we use the Hamming distance to generate a sequence of numerical matrices. We then further investigate the properties of the numerical matrices and show that they are d...

A Raptor code is a concatenation of a fixed rate precode and a Luby-Transform (LT) code that can be used as a rateless error-correcting code over communication channels. By definition, Raptor codes are characterized by irregularity features such as dynamic rate, check-degree variability, and joint coding, which make the design of hardware-efficient decoders a challenging task. In this paper, se...

by a quasi-permutation matrix we mean a square matrix over the complex field c with non-negative integral trace. thus every permutation matrix over c is a quasipermutation matrix. for a given finite group g, let p(g) denote the minimal degree of a faithful permutation representation of g (or of a faithful representation of g by permutation matrices), let q(g) denote the minimal degree of a fait...

Packet demultiplexing and analysis is a core concern for network security, and has hence inspired numerous optimisation attempts since their conception in early packet demultiplexing filters such as CSPF and BPF. These optimisations have generally, but not exclusively, focused on improving the speed of packet classification. Despite these improvements however, packet filters require further opt...

This work introduces a proficient method to build a newly proposed code, named diagonal permutation shifting (DPS) code for the spectral-amplitude-coding (SAC) optical code-division multiple-access (OCDMA) system. The DPS code is derived and constructed from well-known prime codes and certain matrix operations. This proposed code possesses numerous properties such as the cross-correlation (CC) ...

An (n, d, k)-mapping f is a mapping from binary vectors of length n to permutations of length n + k such that for all x, y ∈ {0, 1}n , dH ( f (x), f (y)) ≥ dH (x, y) + d , if dH (x, y) ≤ (n+k)−d and dH ( f (x), f (y)) = n+k, if dH (x, y) > (n+k)−d . In this paper, we construct an (n, 3, 2)-mapping for any positive integer n ≥ 6. An (n, r)-permutation array is a permutation array of length n and...

In this paper we describe a variation of the classical permutation decoding algorithm that can be applied to any affine-invariant code with respect certain type information sets. particular, apply it family first-order Reed-Muller codes sets introduced in [2]. Using improve considerably number errors correct comparison known results topic.

We examine some self-orthogonal codes constructed from a rank-5 primitive permutation representation of degree 1100 of the sporadic simple group HS of HigmanSims. We show that Aut(C) = HS:2, where C is a code of dimension 21 associated with Higman’s geometry.

Weanalyse a probabilistic argument that gives a semi-random construction for a permutation code on n symbols with distance n− s and size (s!(log n)1/2), and a bound on the covering radius for sets of permutations in terms of a certain frequency parameter.