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We define additive skew G-codes over finite fields and discuss several dualities attached to these codes. We examine the properties of self-dual skew G-codes and in particular we show that the dual, under any duality, of an additive skew G-code is also an additive skew G-code. Additionally, we propose a matrix construction for additive skew G-codes and use it to construct several examples of extremal self-dual additive skew G-codes over the finite field F 4 . Such codes have a strong connection to quantum error correcting codes. [ABSTRACT FROM AUTHOR]

In this work, we study codes generated by elements that come from group matrix rings. We present a matrix construction which we use to generate codes in two different ambient spaces: the matrix ring M k (R) and the ring R, where R is the commutative Frobenius ring. We show that codes over the ring M k (R) are one sided ideals in the group matrix ring M k (R) G and the corresponding codes over the ring R are G k -codes of length kn. Additionally, we give a generator matrix for self-dual codes, which consist of the mentioned above matrix construction. We employ this generator matrix to search for binary self-dual codes with parameters [72, 36, 12] and find new singly-even and doubly-even codes of this type. In particular, we construct 16 new Type I and 4 new Type II binary [72, 36, 12] self-dual codes. [ABSTRACT FROM AUTHOR]

We describe skew G-codes, which are codes that are the ideals in a skew group ring, where the ring is a finite commutative Frobenius ring and G is an arbitrary finite group. These codes generalize many of the well-known classes of codes such as cyclic, quasicyclic, constacyclic codes, skew cyclic, skew quasicyclic and skew constacyclic codes. Additionally, using the skew G-matrices, we can generalize almost all the known constructions in the literature for self-dual codes. [ABSTRACT FROM AUTHOR]

We study additive codes with 1-rank hulls and examine their properties for various dualities of the finite field of order 4. We give several constructions of additive and linear codes with 1-rank hulls. We also relate these codes to additive complementary dual codes (ACD). We give an interesting non-existence result for additive codes with a 1-rank hull for the duality M2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$M_2$$\end{document} in terms of the parity of the number of generators. We conclude by giving substantive computations finding codes with one-rank hulls for small lengths using our results. [ABSTRACT FROM AUTHOR]

In this paper, we study dihedral codes with 1-dimensional hulls and we determine precisely when dihedral codes over finite fields with 1-dimensional hulls exist. Moreover, we show that these codes come canonically in pairs. We also introduce 1-dimensional linear complementary pairs of dihedral codes and examine the properties of this class of codes. As an application, we obtain 1-dimensional linear complementary pair of dihedral codes, which are either optimal or near optimal. [ABSTRACT FROM AUTHOR]

The future success of cancer gene therapy is critically dependent upon the development of safe, practical and effective targeting strategies. In this study, we describe a novel and broadly applicable targeting approach in which the induction of apoptotic tumor cell death is linked to the differential expression within the tumor microenvironment of elevated levels of the pro-angiogenic cytokine vascular endothelial growth factor (VEGF). As VEGF is generally absent or produced at only low levels in most normal tissues, undesirable toxicity will not result even if the therapeutic gene in question is inadvertently expressed in non-targeted tissue sites. The basic approach makes use of a chimeric cell-surface protein in which the membrane-spanning and cytoplasmic ‘death domain’ of the pro-apoptotic protein Fas are fused in frame to the extracellular ligand-binding domain of the VEGF receptor Flk-1/KDR/VEGFR2 (Flk-1/Fas). The resultant chimeric Flk-1/Fas receptor was found to be stable and capable of inducing a rapid apoptotic response when expressed in tumor cells that produce endogenous VEGF. Importantly, in the absence of VEGF, transduced tumor cells remain viable although they can be triggered to die by the addition of recombinant VEGF. Given the key role played by VEGF in tumor development and progression, it is proposed that the Flk-1/Fas chimera may have great potential in the context of tumor cell-targeted cancer gene therapy.Cancer Gene Therapy (2009) 16, 279–290; doi:10.1038/cgt.2008.72; published online 26 September 2008 [ABSTRACT FROM AUTHOR]