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
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
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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 âªe on the set {0,1,â¦,pm-1}. From the relation âªe, we derive a partial order ⺠in U={0,1,â¦,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,âº) 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
Journal: Journal of Combinatorial Theory, Series A - Volume 110, Issue 1, April 2005, Pages 71-95
نویسندگان
Xiang-Dong Hou,