New extremal binary self-dual codes from F4+uF4-lifts of quadratic circulant codes over F4
نویسندگان
چکیده
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 کاملNew self-dual additive F4-codes constructed from circulant graphs
In order to construct quantum [[n, 0, d]] codes for (n, d) = (56, 15), (57, 15), (58, 16), (63, 16), (67, 17), (70, 18), (71, 18), (79, 19), (83, 20), (87, 20), (89, 21), (95, 20), we construct self-dual additive F4-codes of length n and minimum weight d from circulant graphs. The quantum codes with these parameters are constructed for the first time.
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 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 کاملNew extremal binary self-dual codes of length 68 from quadratic residue codes over 𝔽2 + u𝔽2 + u2𝔽2
In this correspondence, we consider quadratic double and bordered double circulant construction methods over the ring R := F2 + uF2 + uF2, where u = 1. Among other examples, extremal binary self-dual codes of length 66 are obtained by these constructions. These are extended by using extension theorems for self-dual codes and as a result 8 new extremal binary self-dual codes of length 68 are obt...
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2015
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2015.05.004