By considering two important factors involved in the codon-anticodon interactions, the hydrogen bond number and the chemical type of bases, a codon array of the genetic code table as an increasing code scale of interaction energies of amino acids in proteins was obtained. Next, in order to consecutively obtain all codons from the codon AAC, a sum operation has been introduced in the set of codo...

Problem statement: Cryptosystem using linear codes was developed in 1978 by Mc-Eliece. Later in 1985 Niederreiter and others developed a modified version of cryptosystem using concepts of linear codes. But these systems were not used frequently because of its larger key size. In this study we were designing a cryptosystem using the concepts of algebraic geometric codes with smaller key size. Er...

In this study, an efficient and fast algebraic decoding algorithm (ADA) for the binary systematic quadratic residue (QR) code of length 73 with the reducible generator polynomial to correct up to six errors is proposed. The S(I, J ) matrix method given by He et al. (2001) is utilised to compute the unknown syndromes S5. A technique called swap base is proposed to correct the weight-4 error patt...

The Gilbert type bound for codes in the title is reviewed, both for small and large alphabets. Constructive lower bounds better than these existential bounds are derived from geometric codes, either over Fp or Fp2 , or over even degree extensions of Fp. In the latter case the approach is concatenation with a good code for the Hamming metric as outer code and a short code for the Lee metric as a...

This paper reports the analysis of an industrial implementation of the session-layer of a load-balancing software system. This software comprises 7.5 thousand lines of C code. It is used for distribution of the print jobs among several document processors (workers). A large part of this commercially used software system has been modeled closely and analyzed using process-algebraic techniques. S...

Packet erasure codes are today a real alternative to replication in fault tolerant distributed storage systems. In this paper, we propose the Mojette erasure code based on the Mojette transform, a formerly tomographic tool. The performance of coding and decoding are compared to the Reed-Solomon code implementations of the two open-source reference libraries namely ISA-L and Jerasure 2.0. Result...

From a rational convex polytope of dimension r ≥ 2 J.P. Hansen constructed an error correcting code of length n = (q−1)r over the finite field Fq. A rational convex polytope is the same datum as a normal toric variety and a Cartier divisor. The code is obtained evaluating rational functions of the toric variety defined by the polytope at the algebraic torus, and it is an evaluation code in the ...

A linear code with a complementary dual (or an LCD code) is defined to be a linear code C whose dual code C⊥ satisfies C ∩ C⊥ = {0}. The algebraic characterization of LCD codes is given, and it is shown that asymptotically good LCD codes exist. LCD codes are shown to provide an optimum linear coding solution for the two-user binary adder channel. The nearest-neighbor (or maximum-likelihood) dec...

This article aims to explore the bridge between the algebraic structure of a linear code and the complete decoding process. To this end, we associate a specific binomial ideal I+(C) to an arbitrary linear code. The binomials involved in the reduced Gröbner basis of such an ideal relative to a degreecompatible ordering induce a uniquely defined test-set for the code, and this allows the descript...

The block layered space-time codes, with the intent of simultaneously achieving high coding gain and high code rate, have been suggested. These codes are based on the design principles of existing layered space-time codes and space-time block codes. The previously known concept of a layer has been modified to a block layer wherein a block layer has more than one antenna transmitting at the same...