MinT - Information on Result #2705098

Information on Result #2705098

Linear OOA(64⁴⁰, large, F₆₄, 3, 7), using 1 times NRT-code embedding in larger space based on linear OOA(64³⁷, large, F₆₄, 3, 7), 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(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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(64⁴¹, large, F₆₄, 3, 7)	[i]		OOA Duplication
2	Linear OOA(64⁴², large, F₆₄, 3, 7)	[i]		OOA Duplication