New extremal self-dual codes of lengths 36 and 38
نویسنده
چکیده
There are two distinct weight enumerators for extremal singly-even self-dual [36; 18; 8] codes. For each weight enumerator, only one extremal self-dual code is previously known. In this correspondence, we construct several new extremal singly-even self-dual [36; 18; 8] codes for each weight enumerator. We also construct a number of new extremal singly-even self-dual [38; 19; 8] codes.
منابع مشابه
Classification of extremal and $s$-extremal binary self-dual codes of length 38
Abstract—In this paper we classify all extremal and s-extremal binary self-dual codes of length 38. There are exactly 2744 extremal [38, 19, 8] self-dual codes, two s-extremal [38, 19, 6] codes, and 1730 s-extremal [38, 19, 8] codes. We obtain our results from the use of a recursive algorithm used in the recent classification of all extremal self-dual codes of length 36, and from a generalizati...
متن کاملConstruction of new extremal self-dual codes
In this paper, new binary extremal self-dual codes are presented. A number of new extremal singly-even self-dual codes of lengths 48; 64 and 78, and extremal doubly-even self-dual codes of lengths 80 and 88, are constructed. We also relate an extremal doubly-even self-dual code of length divisible by 24 to an extremal singly-even self-dual code of that length. New singly-even self-dual codes of...
متن کاملClassification of Extremal and -Extremal Binary Self-Dual Codes of Length 38
In this paper we classify all extremal and -extremal binary self-dual codes of length 38. There are exactly 2744 extremal self-dual codes, two -extremal codes, and 1730 -extremal codes. We obtain our results from the use of a recursive algorithm used in the recent classification of all extremal self-dual codes of length 36, and from a generalization of this recursive algorithm for the shadow. T...
متن کاملNew extremal singly even self-dual codes of lengths 64 and 66
For lengths 64 and 66, we construct extremal singly even self-dual codes with weight enumerators for which no extremal singly even selfdual codes were previously known to exist. We also construct new 40 inequivalent extremal doubly even self-dual [64, 32, 12] codes with covering radius 12 meeting the Delsarte bound.
متن کاملNew extremal binary self-dual codes of lengths 66 and 68 from codes over r_k, m
In this work, four circulant and quadratic double circulant (QDC) constructions are applied to the family of the rings R k,m. Self-dual binary codes are obtained as the Gray images of self-dual QDC codes over R k,m. Extremal binary self-dual codes of length 64 are obtained as Gray images of λ-four circulant codes over R 2,1 and R 2,2. Extremal binary self-dual codes of lengths 66 and 68 are con...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- IEEE Trans. Information Theory
دوره 45 شماره
صفحات -
تاریخ انتشار 1999