MinT - Information on Result #2705083

Information on Result #2705083

Linear OOA(64⁴⁸, large, F₆₄, 3, 6), using 5 times NRT-code embedding in larger space based on linear OOA(64³³, large, F₆₄, 3, 6), using

generalized (u,Â u+v)-construction [i] based on
1. 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]
2. 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]
3. linear OOA(64²¹, 2796201, F₆₄, 3, 6) (dual of [(2796201, 3), 8388582, 7]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(64²¹, large, F₆₄, 6) (dual of [large, large−21, 7]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [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.