MinT - Information on Result #989069

Information on Result #989069

Linear OOA(64³², 4194301, F₆₄, 3, 7) (dual of [(4194301, 3), 12582871, 8]-NRT-code), using OOA 2-folding based on linear OOA(64³², 8388602, F₆₄, 2, 7) (dual of [(8388602, 2), 16777172, 8]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. 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]
2. linear OOA(64²⁵, 4194301, F₆₄, 2, 7) (dual of [(4194301, 2), 8388577, 8]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(64²⁵, 8388602, F₆₄, 7) (dual of [8388602, 8388577, 8]-code), using
    - discarding factors / shortening the dual code 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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(8⁶⁴, 8388602, F₈, 3, 7) (dual of [(8388602, 3), 25165742, 8]-NRT-code)	[i]		Trace Code for OOAs