MinT - Information on Result #1683671

Information on Result #1683671

Linear OOA(2¹⁷⁹, 2097191, F₂, 7, 14) (dual of [(2097191, 7), 14680158, 15]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁷⁹, 2097191, F₂, 4, 14) (dual of [(2097191, 4), 8388585, 15]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2¹⁸, 41, F₂, 4, 7) (dual of [(41, 4), 146, 8]-NRT-code), using
  - extracting embedded OOA [i] based on digital (11, 18, 41)-net over F₂, using
    - linear code embedding found in a computer search [i]
2. linear OOA(2¹⁶¹, 2097150, F₂, 4, 14) (dual of [(2097150, 4), 8388439, 15]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(2¹⁶¹, 8388600, F₂, 14) (dual of [8388600, 8388439, 15]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹⁶¹, large, F₂, 14) (dual of [large, large−161, 15]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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(2¹⁷⁹, 2097190, F₂, 8, 14) (dual of [(2097190, 8), 16777341, 15]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2¹⁷⁹, 2097190, F₂, 21, 14) (dual of [(2097190, 21), 44040811, 15]-NRT-code)	[i]		OOA Stacking with Additional Row