MinT - Information on Result #1690998

Information on Result #1690998

Linear OOA(2¹⁷⁷, 2097177, F₂, 8, 14) (dual of [(2097177, 8), 16777239, 15]-NRT-code), using OOA stacking with additional row based on linear OOA(2¹⁷⁷, 2097178, F₂, 7, 14) (dual of [(2097178, 7), 14680069, 15]-NRT-code), using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹⁷⁷, 2097178, F₂, 4, 14) (dual of [(2097178, 4), 8388535, 15]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹⁶, 28, F₂, 4, 7) (dual of [(28, 4), 96, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (9, 16, 28)-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

None.