MinT - Information on Result #1692689

Information on Result #1692689

Linear OOA(2¹⁰⁵, 4140507, F₂, 8, 8) (dual of [(4140507, 8), 33123951, 9]-NRT-code), using appending kth column based on linear OOA(2¹⁰⁵, 4140507, F₂, 7, 8) (dual of [(4140507, 7), 28983444, 9]-NRT-code), using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹⁰⁵, 4140507, F₂, 2, 8) (dual of [(4140507, 2), 8280909, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹⁰⁵, 4194381, F₂, 2, 8) (dual of [(4194381, 2), 8388657, 9]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2¹³, 80, F₂, 2, 4) (dual of [(80, 2), 147, 5]-NRT-code), using
      - extracting embedded OOA [i] based on digital (9, 13, 80)-net over F₂, using
        linear code embedding found in a computer search [i]
    2. linear OOA(2⁹², 4194301, F₂, 2, 8) (dual of [(4194301, 2), 8388510, 9]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(2⁹², 8388602, F₂, 8) (dual of [8388602, 8388510, 9]-code), using
        discarding factors / shortening the dual code based on linear OA(2⁹², large, F₂, 8) (dual of [large, large−92, 9]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [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	Digital (97, 105, 4140507)-net over F₂	[i]		Net Defined by OOA