MinT - Information on Result #1017588

Information on Result #1017588

Linear OOA(64³⁷, 5608932, F₆₄, 3, 7) (dual of [(5608932, 3), 16826759, 8]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64⁷, large, F₆₄, 3, 3), using
- appending kth column [i] based on linear OOA(64⁷, large, F₆₄, 2, 3), using
  - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(64⁷, large, F₆₄, 3) (dual of [large, large−7, 4]-code), using
    - product of projective cap with 64²-ovoid cap in AG(3,Â 64) [i] based on linear OA(64⁴, 4097, F₆₄, 3) (dual of [4097, 4093, 4]-code or 4097-cap in PG(3,64)), using
      - ovoid in PG(3,Â 64) [i]
linear OOA(64³⁰, 2804466, F₆₄, 3, 7) (dual of [(2804466, 3), 8413368, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(64⁵, 8265, F₆₄, 3, 3) (dual of [(8265, 3), 24790, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(64⁵, 8265, F₆₄, 2, 3) (dual of [(8265, 2), 16525, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(64⁵, 8265, F₆₄, 3) (dual of [8265, 8260, 4]-code or 8265-cap in PG(4,64)), using
        large caps in PG(4,Â b) [i]
  2. 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.

Other Results with Identical Parameters

None.

Depending Results

None.