We report weaknesses in two algebraic constructions of low-density parity-check codes based on expander graphs. The Margulis construction gives a code with nearcodewords, which cause problems for the sum-product decoder; The RamanujanMargulis construction gives a code with low-weight codewords, which produce an error-floor.

A cyclic code is associated with another cyclic code to bound its minimum distance. The algebraic relation between these two codes allows the formulation of syndromes and a key equation. In this contribution, we outline the decoding approach for the case of errors and erasures and show how the Extended Euclidean Algorithm can be used for decoding.

SUMMARY In this paper, we give a new lower bound for the dimension of subeld subcodes. This bound improves the lower bound given by Stichtenoth. A BCH code and a subeld subcode of algebraic geometric code on a hyper elliptic curve are discussed as special cases.

The quality of an algebraic geometry code depends on the curve from which the code has been defined. In this paper we consider codes obtained from Castle curves, namely those whose number of rational points attains Lewittes’ bound for some rational point Q and the Weierstrass semigroup at Q is symmetric.

The organization of the canonical genetic code needs to be thoroughly illuminated. Here we reorder the four nucleotides-adenine, thymine, guanine and cytosine-according to their emergence in evolution, and apply the organizational rules to devising an algebraic representation for the canonical genetic code. Under a framework of the devised code, we quantify codon and amino acid usages from a la...

This paper proposes an algebraic decoding algorithm for the (41, 21, 9) quadratic residue code via Lagrange interpolation formula to determine error check and error locator polynomials. Programs written in C++ language have been executed to check every possible error pattern of this quadratic residue code.

In this article, a differential construction for the dual of an algebraic-geometric code on a projective surface is given. Afterwards, this result is used to lower bound the minimum distance of this dual code. The found bounds involve intersection numbers of some particular divisors on the surface. AMS Classification: 14J20, 94B27, 11G25.

Network latency distributions, their algebra, and use examples. This paper considers modeling of capacity-insensitive processes distributed systems. It provides algebraic properties the distribution algebra Haskell code to implement model.

This study presents a novel means of shortening a Reed Solomon (RS) code at the bit level, yielding only shortened BCH subcodes. With the use of a certain basis, an RS codes over ) 2 ( m GF is mapped onto a binary image[4], which contains m concatenated BCH sub-codewords and some glue-vector codewords. With the proposed approach, there only exist some shortened BCH subcode generators in the dia...

Cryptographic Boolean functions must be complex to satisfy Shannon’s principle of confusion. But the cryptographic viewpoint on complexity is not the same as in circuit complexity. The two main criteria evaluating the cryptographic complexity of Boolean functions on F n 2 are the nonlinearity (and more generally the r-th order nonlinearity, for every positive r < n) and the algebraic degree. Tw...