MinT - Information on Result #1191144

Information on Result #1191144

Digital (51, 58, 5605921)-net over F₈, using net defined by OOA based on linear OOA(8⁵⁸, 5605921, F₈, 9, 7) (dual of [(5605921, 9), 50453231, 8]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(8⁵⁸, 5605922, F₈, 3, 7) (dual of [(5605922, 3), 16817708, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8⁸, 13520, F₈, 3, 3) (dual of [(13520, 3), 40552, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(8⁸, 13520, F₈, 2, 3) (dual of [(13520, 2), 27032, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(8⁸, 13520, F₈, 3) (dual of [13520, 13512, 4]-code or 13520-cap in PG(7,8)), using
        product of projective cap with cap in AG(4,Â 8) [i] based on linear OA(8⁴, 65, F₈, 3) (dual of [65, 61, 4]-code or 65-cap in PG(3,8)), using
        ovoid in PG(3,Â 8) [i]
  2. linear OOA(8⁵⁰, 5592402, F₈, 3, 7) (dual of [(5592402, 3), 16777156, 8]-NRT-code), using
    - trace code [i] based on linear OOA(64²⁵, 2796201, F₆₄, 3, 7) (dual of [(2796201, 3), 8388578, 8]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(64²⁵, large, F₆₄, 7) (dual of [large, large−25, 8]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (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, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.