MinT - Information on Result #1072007

Information on Result #1072007

Linear OOA(256⁶, large, F₂₅₆, 4, 3), using appending 1 arbitrary column based on linear OOA(256⁶, large, F₂₅₆, 3, 3), using

appending kth column [i] based on linear OOA(256⁶, large, F₂₅₆, 2, 3), using
- OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(256⁶, large, F₂₅₆, 3) (dual of [large, large−6, 4]-code), using
  - product of projective cap with (hyper)oval [i] based on linear OA(256⁴, 65537, F₂₅₆, 3) (dual of [65537, 65533, 4]-code or 65537-cap in PG(3,256)), using
    - ovoid in PG(3,Â 256) [i]

Mode: Constructive and linear.

Show details for fixed k and m, k and t, m and t.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(256¹⁰, large, F₂₅₆, 4, 3)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(256¹⁴, large, F₂₅₆, 4, 3)	[i]
3	Linear OOA(256¹⁸, large, F₂₅₆, 4, 3)	[i]
4	Linear OOA(256²², large, F₂₅₆, 4, 3)	[i]
5	Linear OOA(256²⁶, large, F₂₅₆, 4, 3)	[i]
6	Linear OOA(256³⁴, large, F₂₅₆, 4, 3)	[i]
7	Linear OOA(256³⁸, large, F₂₅₆, 4, 3)	[i]
8	Linear OOA(256⁴², large, F₂₅₆, 4, 3)	[i]
9	Linear OOA(256⁴⁶, large, F₂₅₆, 4, 3)	[i]
10	Linear OOA(256⁵⁴, large, F₂₅₆, 4, 3)	[i]
11	Linear OOA(256⁵⁸, large, F₂₅₆, 4, 3)	[i]
12	Linear OOA(256⁶², large, F₂₅₆, 4, 3)	[i]
13	Linear OOA(256⁶⁶, large, F₂₅₆, 4, 3)	[i]
14	Linear OOA(256⁷, large, F₂₅₆, 4, 3)	[i]	OOA Duplication
15	Linear OOA(256⁸, large, F₂₅₆, 4, 3)	[i]
16	Linear OOA(256⁹, large, F₂₅₆, 4, 3)	[i]
17	Linear OOA(256²⁷, large, F₂₅₆, 4, 6)	[i]	(u,Â u+v)-Construction for OOAs
18	Linear OOA(256³⁰, large, F₂₅₆, 4, 7)	[i]	(u,Â u+v)-Construction for OOAs
19	Linear OOA(256⁶⁸, large, F₂₅₆, 4, 12)	[i]	Generalized (u,Â u+v)-Construction for OOAs
20	Linear OOA(256⁶⁶, 8388600, F₂₅₆, 4, 12) (dual of [(8388600, 4), 33554334, 13]-NRT-code)	[i]
21	Linear OOA(256⁵⁰, 6291450, F₂₅₆, 4, 11) (dual of [(6291450, 4), 25165750, 12]-NRT-code)	[i]
22	Linear OOA(256⁴⁷, 6291450, F₂₅₆, 4, 10) (dual of [(6291450, 4), 25165753, 11]-NRT-code)	[i]