MinT - Information on Result #2705053

Information on Result #2705053

Linear OOA(64⁴⁰, large, F₆₄, 3, 5), using 64² times duplication based on linear OOA(64³⁸, large, F₆₄, 3, 5), using

strength reduction [i] based on linear OOA(64³⁸, large, F₆₄, 3, 7), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(64¹, 2796201, F₆₄, 3, 1) (dual of [(2796201, 3), 8388602, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64¹, s, F₆₄, 3, 1) for arbitrarily large s, using
      - appending 2 arbitrary columns [i] based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  2. linear OOA(64⁵, 2796201, F₆₄, 3, 2) (dual of [(2796201, 3), 8388598, 3]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁵, large, F₆₄, 3, 2), using
      - appending 1 arbitrary column [i] based on linear OOA(64⁵, large, F₆₄, 2, 2), using
        appending kth column [i] based on linear OA(64⁵, large, F₆₄, 2) (dual of [large, large−5, 3]-code), using
        Hamming code H(5,64) [i]
  3. linear OOA(64⁷, 2796201, F₆₄, 3, 3) (dual of [(2796201, 3), 8388596, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁷, 8388602, F₆₄, 3, 3) (dual of [(8388602, 3), 25165799, 4]-NRT-code), using
      - OOA stacking with additional row [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]
  4. 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 t, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.