کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9515486 1343458 2005 25 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Enumeration of certain affine invariant extended cyclic codes
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
Enumeration of certain affine invariant extended cyclic codes
چکیده انگلیسی
Let p be a prime and let r,e,m be positive integers such that r|e and e|m. Extended cyclic codes of length pm over Fpr which are invariant under AGL(me,Fpe) are characterized by a well-known relation ≪e on the set {0,1,…,pm-1}. From the relation ≪e, we derive a partial order ≺ in U={0,1,…,me(p-1)}e defined by an e-dimensional simplicial cone. We show that the aforementioned extended cyclic codes can be enumerated by the ideals of (U,≺) which are invariant under the rth power of a circulant permutation matrix. When e=2, we enumerate all such invariant ideals by describing their boundaries. Explicit formulas are obtained for the total number of AGL(m2,Fp2)-invariant extended cyclic codes of length pm over Fpr and for the dimensions of such codes. We also enumerate all self-dual AGL(m2,F22)-invariant extended cyclic codes of length 2m over F22 where m2 is odd; the restrictions on the parameters are necessary conditions for the existence of self-dual affine invariant extended cyclic codes with e=2.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series A - Volume 110, Issue 1, April 2005, Pages 71-95
نویسندگان
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