MinT - Information on Result #1019878

Information on Result #1019878

Linear OOA(256²⁰, 2861738, F₂₅₆, 3, 6) (dual of [(2861738, 3), 8585194, 7]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(256⁴, 65537, F₂₅₆, 3, 3) (dual of [(65537, 3), 196607, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(256⁴, 65537, F₂₅₆, 2, 3) (dual of [(65537, 2), 131070, 4]-NRT-code), using
  - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [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]
linear OOA(256¹⁶, 2796201, F₂₅₆, 3, 6) (dual of [(2796201, 3), 8388587, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(256¹⁶, large, F₂₅₆, 6) (dual of [large, large−16, 7]-code), using
  - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	OOA(128²³, 2861738, S₁₂₈, 3, 6)	[i]	Discarding Parts of the Base for OOAs
2	Linear OOA(256²⁶, 5723476, F₂₅₆, 3, 6) (dual of [(5723476, 3), 17170402, 7]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(256⁶¹, 5592918, F₂₅₆, 3, 12) (dual of [(5592918, 3), 16778693, 13]-NRT-code)	[i]
4	Linear OOA(256⁶², 5592920, F₂₅₆, 3, 12) (dual of [(5592920, 3), 16778698, 13]-NRT-code)	[i]
5	Linear OOA(256⁶³, 5593430, F₂₅₆, 3, 12) (dual of [(5593430, 3), 16780227, 13]-NRT-code)	[i]
6	Linear OOA(256⁶⁴, 5593432, F₂₅₆, 3, 12) (dual of [(5593432, 3), 16780232, 13]-NRT-code)	[i]
7	Linear OOA(256⁶⁵, 5636094, F₂₅₆, 3, 12) (dual of [(5636094, 3), 16908217, 13]-NRT-code)	[i]
8	Linear OOA(256⁶⁶, 5636096, F₂₅₆, 3, 12) (dual of [(5636096, 3), 16908222, 13]-NRT-code)	[i]
9	Linear OOA(256⁶⁷, 5636098, F₂₅₆, 3, 12) (dual of [(5636098, 3), 16908227, 13]-NRT-code)	[i]
10	Linear OOA(256⁶⁸, 5658194, F₂₅₆, 3, 12) (dual of [(5658194, 3), 16974514, 13]-NRT-code)	[i]
11	Linear OOA(256⁶⁴, 5592918, F₂₅₆, 3, 13) (dual of [(5592918, 3), 16778690, 14]-NRT-code)	[i]
12	Linear OOA(256⁶⁵, 5592920, F₂₅₆, 3, 13) (dual of [(5592920, 3), 16778695, 14]-NRT-code)	[i]
13	Linear OOA(256⁶⁶, 5593430, F₂₅₆, 3, 13) (dual of [(5593430, 3), 16780224, 14]-NRT-code)	[i]
14	Linear OOA(256⁶⁷, 5593432, F₂₅₆, 3, 13) (dual of [(5593432, 3), 16780229, 14]-NRT-code)	[i]
15	Linear OOA(256⁶⁸, 5636094, F₂₅₆, 3, 13) (dual of [(5636094, 3), 16908214, 14]-NRT-code)	[i]
16	Linear OOA(256²⁰, 2861737, F₂₅₆, 4, 6) (dual of [(2861737, 4), 11446928, 7]-NRT-code)	[i]	OOA Stacking with Additional Row
17	Linear OOA(256²⁰, 2861737, F₂₅₆, 5, 6) (dual of [(2861737, 5), 14308665, 7]-NRT-code)	[i]
18	Linear OOA(256²⁰, 2861737, F₂₅₆, 6, 6) (dual of [(2861737, 6), 17170402, 7]-NRT-code)	[i]