International Journal of Information and Coding Theory (5 papers in press)
Regular Issues
 $\mathbb{Z}_p\mathbb{Z}_p[u]$Additive cyclic codes
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 $\mathbb{Z}_p[x]/(x^\alpha1)\times \mathbb{Z}_p[u][x]/(x^\beta1)$, 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 $\mathbb{Z}_p[x]/(x^\alpha1)\times \mathbb{Z}_p[u][x]/(x^\beta1)$. 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
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 bestknown 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 nonchain ring and their Gray images
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 nonchain 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, selfdual, isodual, selforthogonal 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 duadiccodes; triadic codes; Gray map; selfdual and selforthogonal codes; isodual codes; LCD codes.
 Coding theory: the unitderive methodology
by Ted Hurley, Donny Hurley Abstract: The unitderived 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 unitderived 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; unitderived scheme; decoding.
 Skew cyclic codes over $mathbb{F}_{p}+umathbb{F}_{p}$
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 quasitwisted
codes. We also present several examples of optimal codes. Keywords: skew cyclic codes; optimal codes; codes over rings.
