کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8902852 1632394 2018 7 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the additive cyclic structure of quasi-cyclic codes
ترجمه فارسی عنوان
در ساختار چرخه افزایشی کدهای نیمه چرخه ای
کلمات کلیدی
کد تقریبا چرخه ای، کد حلقه افزایشی،
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
چکیده انگلیسی
An index ℓ, length mℓ quasi-cyclic code can be viewed as a cyclic code of length m over the field Fqℓ via a basis of the extension Fqℓ∕Fq. However, this cyclic code is only linear over Fq, making it an additive cyclic code, or an Fq-linear cyclic code, over the alphabet Fqℓ. This approach was recently used in Shi et al. (2017) [16] to study a class of quasi-cyclic codes, and more importantly in Shi et al. (2017) [17] to settle a long-standing question on the asymptotic performance of cyclic codes. Here, we answer one of the problems posed in these two articles, and characterize those quasi-cyclic codes which have Fqℓ-linear cyclic images under a basis of the extension Fqℓ∕Fq. Our characterizations are based on the module structure of quasi-cyclic codes, as well as on their CRT decompositions into constituents. In the case of a polynomial basis, we characterize the constituents by using the theory of invariant subspaces of operators. We also observe that analogous results extend to the case of quasi-twisted codes.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 341, Issue 10, October 2018, Pages 2735-2741
نویسندگان
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