MinT - Information on Result #1195314

Information on Result #1195314

Digital (68, 84, 131077)-net over F₁₆, using net defined by OOA based on linear OOA(16⁸⁴, 131077, F₁₆, 18, 16) (dual of [(131077, 18), 2359302, 17]-NRT-code), using

OOA 4-folding and stacking with additional row [i] based on linear OOA(16⁸⁴, 524309, F₁₆, 2, 16) (dual of [(524309, 2), 1048534, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(16⁸⁴, 524311, F₁₆, 2, 16) (dual of [(524311, 2), 1048538, 17]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(16⁹, 24, F₁₆, 2, 8) (dual of [(24, 2), 39, 9]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,39P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
        a function field by SÃ©mirat [i]
    2. linear OOA(16⁷⁵, 524287, F₁₆, 2, 16) (dual of [(524287, 2), 1048499, 17]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(16⁷⁵, 1048574, F₁₆, 16) (dual of [1048574, 1048499, 17]-code), using
        discarding factors / shortening the dual code based on linear OA(16⁷⁵, 1048575, F₁₆, 16) (dual of [1048575, 1048500, 17]-code), using
        1 times truncation [i] based on linear OA(16⁷⁶, 1048576, F₁₆, 17) (dual of [1048576, 1048500, 18]-code), using
        an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.