MinT - Information on Result #1022005

Information on Result #1022005

Linear OOA(8¹³⁷, 5592808, F₈, 3, 15) (dual of [(5592808, 3), 16778287, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8²³, 406, F₈, 3, 7) (dual of [(406, 3), 1195, 8]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(8¹, 73, F₈, 3, 1) (dual of [(73, 3), 218, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8¹, s, F₈, 3, 1) for arbitrarily large s, using
      - appending 2 arbitrary columns [i] based on linear OA(8¹, s, F₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  2. linear OOA(8³, 73, F₈, 3, 2) (dual of [(73, 3), 216, 3]-NRT-code), using
    - appending 1 arbitrary column [i] based on linear OOA(8³, 73, F₈, 2, 2) (dual of [(73, 2), 143, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(8³, 73, F₈, 2) (dual of [73, 70, 3]-code), using
        Hamming code H(3,8) [i]
  3. linear OOA(8⁵, 130, F₈, 3, 3) (dual of [(130, 3), 385, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8⁵, 207, F₈, 3, 3) (dual of [(207, 3), 616, 4]-NRT-code), using
      - OOA stacking with additional row [i] based on linear OA(8⁵, 208, F₈, 3) (dual of [208, 203, 4]-code or 208-cap in PG(4,8)), using
        caps completed using a computer search [i]
  4. linear OOA(8¹⁴, 130, F₈, 3, 7) (dual of [(130, 3), 376, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (7, 14, 130)-net over F₈, using
      - trace code for nets [i] based on digital (0, 7, 65)-net over F₆₄, using
        net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
        the rational function field F₆₄(x) [i]
        Niederreiter sequence [i]
linear OOA(8¹¹⁴, 5592402, F₈, 3, 15) (dual of [(5592402, 3), 16777092, 16]-NRT-code), using
- trace code [i] based on linear OOA(64⁵⁷, 2796201, F₆₄, 3, 15) (dual of [(2796201, 3), 8388546, 16]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(64⁵⁷, large, F₆₄, 15) (dual of [large, large−57, 16]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [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.

Other Results with Identical Parameters

None.

Depending Results

None.