کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8895619 | 1630351 | 2018 | 27 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Negacyclic codes over the local ring Z4[v]/ãv2+2vã of oddly even length and their Gray images
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Negacyclic codes over the local ring Z4[v]/ãv2+2vã of oddly even length and their Gray images Negacyclic codes over the local ring Z4[v]/ãv2+2vã of oddly even length and their Gray images](/preview/png/8895619.png)
چکیده انگلیسی
Let R=Z4[v]/ãv2+2vã=Z4+vZ4 (v2=2v) and n be an odd positive integer. Then R is a local non-principal ideal ring of 16 elements and there is a Z4-linear Gray map from R onto Z42 which preserves Lee distance and orthogonality. First, a canonical form decomposition and the structure for any negacyclic code over R of length 2n are presented. From this decomposition, a complete classification of all these codes is obtained. Then the cardinality and the dual code for each of these codes are given, and self-dual negacyclic codes over R of length 2n are presented. Moreover, all 23â
(4p+5â
2p+9)2pâ2p negacyclic codes over R of length 2Mp and all 3â
(4p+5â
2p+9)2pâ1â1p self-dual codes among them are presented precisely, where Mp=2pâ1 is a Mersenne prime. Finally, 36 new and good self-dual 2-quasi-twisted linear codes over Z4 with basic parameters (28,228,dL=8,dE=12) and of type 21447 and basic parameters (28,228,dL=6,dE=12) and of type 21646 which are Gray images of self-dual negacyclic codes over R of length 14 are listed.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Finite Fields and Their Applications - Volume 52, July 2018, Pages 67-93
Journal: Finite Fields and Their Applications - Volume 52, July 2018, Pages 67-93
نویسندگان
Yuan Cao, Yonglin Cao,