کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8895666 | 1630352 | 2018 | 28 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Multi-twisted codes over finite fields and their dual codes
ترجمه فارسی عنوان
کدهای پیچیده چندگانه بر زمینه های محدود و کدهای دوگانه
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
Let Fq denote the finite field of order q, let m1,m2,â¯,mâ be positive integers satisfying gcdâ¡(mi,q)=1 for 1â¤iâ¤â, and let n=m1+m2+â¯+mâ. Let Î=(λ1,λ2,â¯,λâ) be fixed, where λ1,λ2,â¯,λâ are non-zero elements of Fq. In this paper, we study the algebraic structure of Î-multi-twisted codes of length n over Fq and their dual codes with respect to the standard inner product on Fqn. We provide necessary and sufficient conditions for the existence of a self-dual Î-multi-twisted code of length n over Fq, and obtain enumeration formulae for all self-dual and self-orthogonal Î-multi-twisted codes of length n over Fq. We also derive some sufficient conditions under which a Î-multi-twisted code is linear with complementary dual (LCD). We determine the parity-check polynomial of all Î-multi-twisted codes of length n over Fq and obtain a BCH type bound on their minimum Hamming distances. We also determine generating sets of dual codes of some Î-multi-twisted codes of length n over Fq from the generating sets of the codes. Besides this, we provide a trace description for all Î-multi-twisted codes of length n over Fq by viewing these codes as direct sums of certain concatenated codes, which leads to a method to construct these codes. We also obtain a lower bound on their minimum Hamming distances using their multilevel concatenated structure.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Finite Fields and Their Applications - Volume 51, May 2018, Pages 270-297
Journal: Finite Fields and Their Applications - Volume 51, May 2018, Pages 270-297
نویسندگان
Anuradha Sharma, Varsha Chauhan, Harshdeep Singh,