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Group Algebra Codes Define Over Extra-Special p-Group

In: International Conference on Mathematical Sciences and Statistics 2013

Author

Listed:
  • Denis C. K. Wong

    (Universiti Tunku Abdul Rahman, Department of Applied Mathematics and Actuarial Science, Faculty of Engineering and Science)

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.

Suggested Citation

  • Denis C. K. Wong, 2014. "Group Algebra Codes Define Over Extra-Special p-Group," Springer Books, in: Adem Kilicman & Wah June Leong & Zainidin Eshkuvatov (ed.), International Conference on Mathematical Sciences and Statistics 2013, edition 127, pages 119-127, Springer.
    • Handle: RePEc:spr:sprchp:978-981-4585-33-0_13
    DOI: 10.1007/978-981-4585-33-0_13
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