MinT - Information on Result #1014577

Information on Result #1014577

Linear OOA(8¹³⁵, 5592722, F₈, 3, 15) (dual of [(5592722, 3), 16778031, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8²¹, 320, F₈, 3, 7) (dual of [(320, 3), 939, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8⁵, 208, F₈, 3, 3) (dual of [(208, 3), 619, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(8⁵, 208, F₈, 2, 3) (dual of [(208, 2), 411, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [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]
  2. linear OOA(8¹⁶, 160, F₈, 3, 7) (dual of [(160, 3), 464, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (9, 16, 160)-net over F₈, using
      - trace code for nets [i] based on digital (1, 8, 80)-net over F₆₄, using
        net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
        a function field by SÃ©mirat [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.