MinT - Information on Result #1691138

Information on Result #1691138

Linear OOA(2¹⁷⁹, 1677753, F₂, 8, 15) (dual of [(1677753, 8), 13421845, 16]-NRT-code), using OOA stacking with additional row based on linear OOA(2¹⁷⁹, 1677754, F₂, 7, 15) (dual of [(1677754, 7), 11744099, 16]-NRT-code), using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹⁷⁹, 1677754, F₂, 5, 15) (dual of [(1677754, 5), 8388591, 16]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹⁷, 34, F₂, 5, 7) (dual of [(34, 5), 153, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (10, 17, 34)-net over F₂, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(2¹⁶², 1677720, F₂, 5, 15) (dual of [(1677720, 5), 8388438, 16]-NRT-code), using
    - OOA 5-folding [i] based on linear OA(2¹⁶², 8388600, F₂, 15) (dual of [8388600, 8388438, 16]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹⁶², large, F₂, 15) (dual of [large, large−162, 16]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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.