Group Algebra Codes Define Over Extra-Special p-Group

Denis C. K. Wong ()
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Denis C. K. Wong: Universiti Tunku Abdul Rahman, Department of Applied Mathematics and Actuarial Science, Faculty of Engineering and Science

A chapter in International Conference on Mathematical Sciences and Statistics 2013, 2014, pp 119-127 from Springer

Abstract: Abstract In this paper, group algebra code defined over any extra-special p-group G is constructed. If $char(F) \nmid |G|$ , then FG is semisimple and hence $FG = \bigoplus_{e_i \in M} FGe_j$ , where e j is an idempotent of FG and M is the set consisting of all idempotents of FG. Any idea I of FG is a direct sum of some FGe J , say $I = \bigoplus_{k=1}^{t} FGe_{j_k}$ , for some t such that $1 \leq t \leq |G|$ . Let $\beta = \{e_{j_k}\}_{k=1}^t$ and $\mu=M \backslash \beta$ , then I is generated by β and for technical reason, I denotes $I_{\mu} = \{u \in FG \mid ue_{j_r} = 0, \forall e_{j_r} \in \mu\}$ . The idempotent e j provides useful information to determine the minimum distance for this family of group algebra code. Our primary task is to identify all such idempotents and thus construct a family of MDS group algebra code by choosing a suitable subset of μ in order to maximize the minimum distance.

Keywords: Group Algebra; Minimum Distance; Linear Idempotent; Principal Idempotent; Abelian Codes (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-981-4585-33-0_13

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