MinT - Information on Result #1665168

Information on Result #1665168

Linear OOA(2¹⁵⁶, 2152219, F₂, 6, 12) (dual of [(2152219, 6), 12913158, 13]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁵⁶, 2152219, F₂, 3, 12) (dual of [(2152219, 3), 6456501, 13]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁵⁶, 2796265, F₂, 3, 12) (dual of [(2796265, 3), 8388639, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹⁸, 64, F₂, 3, 6) (dual of [(64, 3), 174, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (12, 18, 64)-net over F₂, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(2¹³⁸, 2796201, F₂, 3, 12) (dual of [(2796201, 3), 8388465, 13]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(2¹³⁸, large, F₂, 12) (dual of [large, large−138, 13]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Mode: 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		This result only	Method
1	Linear OOA(2¹⁵⁶, 2152218, F₂, 7, 12) (dual of [(2152218, 7), 15065370, 13]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2¹⁵⁶, 2152218, F₂, 8, 12) (dual of [(2152218, 8), 17217588, 13]-NRT-code)	[i]
3	Linear OOA(2¹⁵⁶, 2152218, F₂, 18, 12) (dual of [(2152218, 18), 38739768, 13]-NRT-code)	[i]