MinT - Information on Result #1191148

Information on Result #1191148

Digital (53, 60, 5862801)-net over F₈, using net defined by OOA based on linear OOA(8⁶⁰, 5862801, F₈, 9, 7) (dual of [(5862801, 9), 52765149, 8]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(8⁶⁰, 5862802, F₈, 3, 7) (dual of [(5862802, 3), 17588346, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8¹⁰, 270400, F₈, 3, 3) (dual of [(270400, 3), 811190, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(8¹⁰, 270400, F₈, 2, 3) (dual of [(270400, 2), 540790, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(8¹⁰, 270400, F₈, 3) (dual of [270400, 270390, 4]-code or 270400-cap in PG(9,8)), using
        product of projective cap with cap in AG(6,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.