MinT - Information on Result #1836619

Information on Result #1836619

OOA(8¹⁵⁷, 5592930, S₈, 3, 17), using (u,Â u+v)-construction based on

OOA(8²⁷, 528, S₈, 3, 8), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8⁵, 14, F₈, 3, 4) (dual of [(14, 3), 37, 5]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,37P) [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14, using
      - F₂ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]
  2. OOA(8²², 514, S₈, 3, 8), using
    - extracting embedded OOA [i] based on (14, 22, 514)-net in base 8, using
      - trace code for nets [i] based on (3, 11, 257)-net in base 64, using
        1 times m-reduction [i] based on (3, 12, 257)-net in base 64, using
        base change [i] based on digital (0, 9, 257)-net over F₂₅₆, using
        net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
        Niederreiter sequence [i]
linear OOA(8¹³⁰, 5592402, F₈, 3, 17) (dual of [(5592402, 3), 16777076, 18]-NRT-code), using
- trace code [i] based on linear OOA(64⁶⁵, 2796201, F₆₄, 3, 17) (dual of [(2796201, 3), 8388538, 18]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(64⁶⁵, large, F₆₄, 17) (dual of [large, large−65, 18]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]

Mode: Constructive.

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.