MinT - Information on Result #1017572

Information on Result #1017572

Linear OOA(64³⁵, large, F₆₄, 3, 6), 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(64²⁸, 5592402, F₆₄, 3, 6) (dual of [(5592402, 3), 16777178, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(64⁷, large, F₆₄, 3, 3) (see above)
  2. 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.

Show details for fixed k and m, k and t, m and t.

None.

The following results depend on this result: