Forthcoming articles

 


International Journal of Information and Coding Theory

 

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International Journal of Information and Coding Theory (6 papers in press)

 

Regular Issues

 

  • An Iterative Decoding Scheme on Random Burst Error Correction with Reed Solomon Codes   Order a copy of this article
    by Xin Gao 
    Abstract: We investigate the decoding scheme of conventional Reed-Solomon (R-S) codes, and propose a systematic model to achieve better decoding results on random burst error corrections. We follow the iterative decoding procedure and verify this decoding model by implementing a typical R-S (15, 9) code, then present the complexity analysis of this decoding model on the improvements for burst error correction. Simulations on several examples of R-S codes display the validity of this decoding scheme.
    Keywords: Reed-Solomon (R-S) code; burst error correction; decoding.

  • Skew cyclic and skew (_1 + u_2 + v_3 + uv_4)-constacyclic codes over F_q + uF_q + vF_q + uvF_q   Order a copy of this article
    by Habibul Islam, Om Prakash 
    Abstract: In this note, we study skew cyclic and skew constacyclic codes over the ring R=F_q+uF_q+vF_q+uvF_q where q=p^m, p is an odd prime, u^2=u, v^2=v, uv=vu. We show that Gray images of a skew cyclic and skew alpha-constacyclic codes of length n over R are skew quasi-cyclic codes of length 4n over F_q of index 4. Also, it is shown that skew alpha-constacyclic codes are either equivalent to alpha-constacyclic codes or alpha-quasi-twisted codes over R. Further, structural properties, specially, generating polynomials and idempotent generators for skew cyclic and skew constacyclic codes are determined by decomposition method.
    Keywords: Skew polynomial ring; skew cyclic code; skew quasi-cyclic code; skew constacyclic code; Gray map; generating polynomial; idempotent generator.

  • Constacyclic codes over the ring F_p+vF_p and their applications of constructing new nonbinary quantum codes   Order a copy of this article
    by Yongkang Wang, Jian Gao 
    Abstract: In this paper, we study some results on constacyclic codes over $mathbb{F}_p+vmathbb{F}_p$, where $p$ is an odd prime and $v^2=v$. Under some special Gray map, the image of the $(alpha+beta v)$-constacyclic code over $mathbb{F}_p+vmathbb{F}_p$ is a $(-alpha(alpha+beta))$-constacyclic code over $mathbb{F}_p$, where $alpha$ and $beta$ are nonzero elements of $mathbb{F}_p$ satisfying $beta=-2alpha$. As an application, some new nonbinary quantum codes are obtained.
    Keywords: Constacyclic codes; Gray map; New nonbinary quantum codes.

  • Self-dual codes over $\Z_4[x]/(x^2+2x)$ and the $\Z_4$-images   Order a copy of this article
    by Bahattin Yildiz, Abidin Kaya 
    Abstract: In this work, constructions for self-dual codes over the ring $\Z_4[x]/(x^2+2x)$ are considered together with their images under an orthogonality-preserving Gray map, which result in self-dual $\Z_4$-codes. Theoretical results about the existence/non-existence of self-dual codes from construction methods such as the double circulant, bordered double circulant and four circulant matrices for the rings $\Z_4$ and $\Z_4[x]/(x^2+2x)$ are given. The construction methods are then applied to get good self-dual $\Z_4$-codes of lengths 16, 32, 48 and 64 (including some extremal Type I and Type II codes), which are tabulated at the end.
    Keywords: self-dual codes; codes over rings; Gray maps;rndouble-circulant codes; bordered double circulant codes; four circulant codes.

  • A study of cyclic and constacyclic codes over Z_{4} + u Z_{4} + vZ_{4}   Order a copy of this article
    by Habibul Islam, Om Prakash 
    Abstract: In this paper, we study some properties of cyclic and constacyclic codes over the ring $R= mathbb{Z}_{4}+umathbb{Z}_{4}+vmathbb{Z}_{4}$ where $u^{2}=v^{2}=uv =vu=0$. The generator polynomials and minimal spanning set for cyclic codes over $R$ are determined. Further, $(1+2u)$-constacyclic codes are considered and find the cyclic, quasi-cyclic and permutation equivalent to a QC code over $mathbb{Z}_{4}$ as the Gray images of $(1+2u)$-constacyclic codes over $R$.
    Keywords: Cyclic code; Minimal spanning set; Constacyclic code; Quasi-cyclic code; Gray map.

  • Quantum error-correcting codes: the unit design strategy   Order a copy of this article
    by Ted Hurley, Donny Hurley, Barry Hurley 
    Abstract: Series of maximum distance quantum error-correcting codes are developed and analysed. For a given rate and given error-correction capability, quantum error-correcting codes with these specifications are constructed. The codes are explicit with efficient decoding algorithms. For a given field maximum length quantum codes are constructed.
    Keywords: Quantum Code; MDS.