MinT - Information on Result #1014247

Information on Result #1014247

Linear OOA(8⁶¹, 6471202, F₈, 3, 7) (dual of [(6471202, 3), 19413545, 8]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8¹¹, 878800, F₈, 3, 3) (dual of [(878800, 3), 2636389, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(8¹¹, 878800, F₈, 2, 3) (dual of [(878800, 2), 1757589, 4]-NRT-code), using
  - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(8¹¹, 878800, F₈, 3) (dual of [878800, 878789, 4]-code or 878800-cap in PG(10,8)), using
    - product of two projective caps and an affine cap avoiding two hyperplanes [i] based on
      1. linear OA(8⁴, 65, F₈, 3) (dual of [65, 61, 4]-code or 65-cap in PG(3,8)), using
        ovoid in PG(3,Â 8) [i]
      2. linear OA(8⁴, 65, F₈, 3) (dual of [65, 61, 4]-code or 65-cap in PG(3,8)) (see above)
linear OOA(8⁵⁰, 5592402, F₈, 3, 7) (dual of [(5592402, 3), 16777156, 8]-NRT-code), using
- trace code [i] based on 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.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(8⁶¹, 6471201, F₈, 9, 7) (dual of [(6471201, 9), 58240748, 8]-NRT-code)	[i]		OOA Stacking with Additional Row