Forthcoming articles

 


International Journal of Information and Coding Theory

 

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International Journal of Information and Coding Theory (5 papers in press)

 

Regular Issues

 

  • $\mathbb{Z}_p\mathbb{Z}_p[u]$-Additive cyclic codes   Order a copy of this article
    by Lingyu Diao, Jian Gao 
    Abstract: Additive cyclic codes of length $(\alpha,\beta)$ over $\mathbb{Z}_p\mathbb{Z}_p[u]$ can be viewed as $\mathbb{Z}_p[u][x]$-submodules of $\mathbb{Z}_p[x]/(x^\alpha-1)\times \mathbb{Z}_p[u][x]/(x^\beta-1)$, where $\mathbb{Z}_p[u]=\mathbb{Z}_p+u\mathbb{Z}_p$, $u^2=0$. In this paper, we determine the generator polynomials and the minimal generating sets of this family of codes as $\mathbb{Z}_p[u]$-submodules of $\mathbb{Z}_p[x]/(x^\alpha-1)\times \mathbb{Z}_p[u][x]/(x^\beta-1)$. Further, we also determine the generator polynomials of the dual codes of $\mathbb{Z}_p\mathbb{Z}_p[u]$-additive cyclic codes. Moreover, some binary quantum codes are constructed by additive cyclic codes over $\mathbb{Z}_2\mathbb{Z}_2[u]$.
    Keywords: additive cyclic codes; minimal generating sets; binary quantum codes.

  • A deterministic algorithm for the distance and weight distribution of binary nonlinear codes   Order a copy of this article
    by Emanuele Bellini, Massimiliano Sala 
    Abstract: Given a binary nonlinear code, we provide a deterministic algorithm to compute its weight and distance distribution, rnand in particular its minimum weight and its minimum distance,rnwhich takes advantage of fast Fourier techniques.rnThis algorithm's performance is similar to that of best-known algorithms for the average case, rnwhile it is especially efficient for codes with low information rate. rnWe provide complexity estimates for several cases of interest.
    Keywords: Distance distribution; minimum distance; weight distribution; minimum weight; nonlinear code.

  • Duadic and Triadic codes over a finite non-chain ring and their Gray images   Order a copy of this article
    by Mokshi Goyal, Madhu Raka 
    Abstract: Let f(u) be a polynomial of degree m, m > or = 2, which splits into distinct linear factors over a finite field F_q. Let R= F_q [u]/< f(u)> be a finite non-chain ring. In this paper, we study duadic codes, their extensions and triadic codes over the ring R. A Gray map from R^n to F_q^{mn} is defined which preserves self duality of linear codes. As a consequence, self-dual, isodual, self-orthogonal and complementary dual(LCD) codes over F_q are constructed. Some examples are also given to illustrate this.
    Keywords: Quadratic residue codes; duadic codes; extended duadic-codes; triadic codes; Gray map; self-dual and self-orthogonal codes; isodual codes; LCD codes.

  • Coding theory: the unit-derive methodology   Order a copy of this article
    by Ted Hurley, Donny Hurley 
    Abstract: The unit-derived method in coding theory is shown to be a unique optimal scheme for constructing and analysing codes. In many cases efficient and practical decoding methods are produced. Codes with efficient decoding algorithms at maximal distances possible are derived from unit schemes. In particular unit-derived codes from Vandermonde or Fourier rn matrices are particularly commendable giving rise to mds codes of varying rates with practical and efficient decoding algorithms. For a given rate and given error correction capability, explicit rn codes with efficient error correcting algorithms are designed to these specifications. An explicit constructive proof with an efficient decoding algorithm is given for Shannon's theorem. For a given finite field, codes are constructed which are `optimal' for this field.
    Keywords: Code; unit-derived scheme; decoding.

  • Skew cyclic codes over $mathbb{F}_{p}+umathbb{F}_{p}$   Order a copy of this article
    by Reza Dastbasteh, Seyyed Hamed Mousavi, Taher Abualrub, Nuh Aydin, Javad Haghighat 
    Abstract: In this paper, we study skew cyclic codes with arbitrary length over the ring $R=\mathbb{F}_{p}+u\mathbb{F}_{p}$ where $p$ is an odd prime and $% u^{2}=0$. We characterize all skew cyclic codes of length $n$ as left $% R[x;\theta ]$-submodules of $R_{n}=R[x;\theta ]/\langle x^{n}-1\rangle $. We find all generator polynomials for these codes and describe their minimal spanning sets. Moreover, an encoding algorithm is presented for skew cyclic codes over the ring $R$. Finally, based on the theory we developed in this paper, we provide examples of codes with good parameters over $F_{p}$ with different odd prime $p.$ In fact, example 6 in our paper is a new ternary code in the class of quasi-twisted codes. We also present several examples of optimal codes.
    Keywords: skew cyclic codes; optimal codes; codes over rings.