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Rank-metric ideal codes in twisted group algebras with involution | ||
| Journal of Algebra and Related Topics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 23 آبان 1405 اصل مقاله (234.94 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2026.34649.1997 | ||
| نویسنده | ||
| P. Nangolo* | ||
| Department of Mathematics and Economics, International University of Management, Nkurenkuru Campus, Windhoek, Namibia | ||
| چکیده | ||
| Let $K=\mathbb F_{q^m}$, let $G$ be a finite group of order $n$, and let $A=K^\alpha[G]$ be a twisted group algebra. We introduce a rank metric on $A$ through the coefficient support over $\mathbb F_q$ and show that, for base-field cocycles, it is recovered from the entries of either regular representation. For a $\sigma$-unitary cocycle we construct a canonical semilinear involution and a nondegenerate coefficient pairing. The orthogonal of an idempotent ideal $Ae$ is proved to be $A(1-e^*)$, yielding criteria for self-orthogonal, self-dual and complementary-dual ideals. The coordinate isometry transfers the rank-metric MacWilliams moment identities to these ideals. Finally, twisted cyclic algebras yield two conditional MRD constructions with parameters $[n,1,n]$ and $[n,n-1,2]$. | ||
| کلیدواژه‌ها | ||
| Twisted group algebra؛ Rank-metric code؛ Involution؛ Ideal code؛ MRD code | ||
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آمار تعداد مشاهده مقاله: 1 تعداد دریافت فایل اصل مقاله: 1 |
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