کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8895648 | 1630352 | 2018 | 14 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Self-dual codes with an automorphism of order 7 and s-extremal codes of length 68
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
This paper studies and classifies optimal binary self-dual codes having an automorphism of order 7 with 9 cycles. This classification is done by applying a method for constructing binary self-dual codes with an automorphism of odd prime order p. There are exactly 69781 inequivalent binary self-dual [64,32,12] codes with an automorphism of type 7â(9,1). As for binary [66,33,12] self-dual codes with an automorphism of type 7â(9,3) there are 1652432 such codes. We also construct more than 4 million new optimal codes of length 68 among which are the first known examples of the very elusive s-extremal self-dual codes. We prove the nonexistence of [70,35,14] codes with an automorphism of type 7â(9,7). Most of the constructed codes for all lengths have weight enumerators for which the existence was not known before.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Finite Fields and Their Applications - Volume 51, May 2018, Pages 17-30
Journal: Finite Fields and Their Applications - Volume 51, May 2018, Pages 17-30
نویسندگان
Nikolay Yankov, Milena Ivanova, Moon Ho Lee,