MinT - Information on Result #3011123

Information on Result #3011123

Linear OOA(2²⁰⁶, 1677759, F₂, 8, 16) (dual of [(1677759, 8), 13421866, 17]-NRT-code), using 2¹ times duplication based on linear OOA(2²⁰⁵, 1677759, F₂, 8, 16) (dual of [(1677759, 8), 13421867, 17]-NRT-code), using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2²⁰⁵, 1677759, F₂, 5, 16) (dual of [(1677759, 5), 8388590, 17]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²¹, 39, F₂, 5, 8) (dual of [(39, 5), 174, 9]-NRT-code), using
    - extracting embedded OOA [i] based on digital (13, 21, 39)-net over F₂, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(2¹⁸⁴, 1677720, F₂, 5, 16) (dual of [(1677720, 5), 8388416, 17]-NRT-code), using
    - OOA 5-folding [i] based on linear OA(2¹⁸⁴, 8388600, F₂, 16) (dual of [8388600, 8388416, 17]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹⁸⁴, large, F₂, 16) (dual of [large, large−184, 17]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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.