On the performance of binary extremal self-dual codes
نویسندگان
چکیده
The decoding error probability of a code C measures the quality of performance when C is used for error correction in data transmission. In this note we compare different types of codes with regard to the decoding error probability.
منابع مشابه
New extremal binary self-dual codes from F4+uF4-lifts of quadratic circulant codes over F4
In this work, quadratic double and quadratic bordered double circulant constructions are applied to F4 + uF4 as well as F4, as a result of which extremal binary self-dual codes of length 56 and 64 are obtained. The binary extension theorems as well as the ring extension version are used to obtain 7 extremal self-dual binary codes of length 58, 24 extremal self-dual binary codes of length 66 and...
متن کاملExtension theorems for self-dual codes over rings and new binary self-dual codes
In this work, extension theorems are generalized to self-dual codes over rings and as applications many new binary self-dual extremal codes are found from self-dual codes over F2m + uF2m for m = 1, 2. The duality and distance preserving Gray maps from F4 + uF4 to (F2 + uF2) and F42 are used to obtain self-dual codes whose binary Gray images are [64, 32, 12]-extremal self-dual. An F2 + uF2-exten...
متن کاملFormally self-dual additive codes over F4 and near-extremal self-dual codes
We introduce a class of formally self-dual additive codes over F4 as a natural analogue of binary formally self-dual codes, which is missing in the study of additive codes over F4. We define extremal formally self-dual additive codes over F4 and classify all such codes. Interestingly, we find exactly three formally self-dual additive (7, 27) odd codes over F4 with minimum distance d = 4, a bett...
متن کاملClassification 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 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 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:
- Adv. in Math. of Comm.
دوره 5 شماره
صفحات -
تاریخ انتشار 2011