MinT - Information on Result #1143460

Information on Result #1143460

Linear OOA(2²⁵⁷, 4194327, F₂, 6, 12) (dual of [(4194327, 6), 25165705, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2¹⁴, 26, F₂, 6, 6) (dual of [(26, 6), 142, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(2¹⁴, 26, F₂, 5, 6) (dual of [(26, 5), 116, 7]-NRT-code), using
  - extracting embedded OOA [i] based on digital (8, 14, 26)-net over F₂, using
    - linear code embedding found in a computer search [i]
linear OOA(2²⁴³, 4194301, F₂, 6, 12) (dual of [(4194301, 6), 25165563, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2²⁴³, 8388602, F₂, 3, 12) (dual of [(8388602, 3), 25165563, 13]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(2²⁴³, large, F₂, 3, 12), using
    - trace code [i] based on linear OOA(8⁸¹, 2796201, F₈, 3, 12) (dual of [(2796201, 3), 8388522, 13]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(8⁸¹, large, F₈, 12) (dual of [large, large−81, 13]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 8⁸âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²⁵⁷, 4194326, F₂, 7, 12) (dual of [(4194326, 7), 29360025, 13]-NRT-code)	[i]	OOA Stacking with Additional Row
2	Linear OOA(2²⁵⁷, 4194326, F₂, 8, 12) (dual of [(4194326, 8), 33554351, 13]-NRT-code)	[i]
3	Linear OOA(2²⁵⁷, 4194326, F₂, 18, 12) (dual of [(4194326, 18), 75497611, 13]-NRT-code)	[i]