MinT - Information on Result #1083695

Information on Result #1083695

Linear OOA(256²⁷, 2097408, F₂₅₆, 4, 8) (dual of [(2097408, 4), 8389605, 9]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(256⁵, 258, F₂₅₆, 4, 4) (dual of [(258, 4), 1027, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(256⁵, 258, F₂₅₆, 3, 4) (dual of [(258, 3), 769, 5]-NRT-code), using
  - extracting embedded OOA [i] based on digital (1, 5, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]
linear OOA(256²², 2097150, F₂₅₆, 4, 8) (dual of [(2097150, 4), 8388578, 9]-NRT-code), using
- OOA 4-folding [i] based on linear OA(256²², 8388600, F₂₅₆, 8) (dual of [8388600, 8388578, 9]-code), using
  - discarding factors / shortening the dual code based on linear OA(256²², large, F₂₅₆, 8) (dual of [large, large−22, 9]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	OOA(128³¹, 2097408, S₁₂₈, 4, 8)	[i]	Discarding Parts of the Base for OOAs
2	Linear OOA(256³⁷, 4194816, F₂₅₆, 4, 8) (dual of [(4194816, 4), 16779227, 9]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(256²⁷, 2097407, F₂₅₆, 5, 8) (dual of [(2097407, 5), 10487008, 9]-NRT-code)	[i]	OOA Stacking with Additional Row
4	Linear OOA(256²⁷, 2097407, F₂₅₆, 6, 8) (dual of [(2097407, 6), 12584415, 9]-NRT-code)	[i]
5	Linear OOA(256²⁷, 2097407, F₂₅₆, 12, 8) (dual of [(2097407, 12), 25168857, 9]-NRT-code)	[i]