MinT - Information on Result #904255

Information on Result #904255

Linear OOA(81¹⁸, 6566, F₈₁, 2, 7) (dual of [(6566, 2), 13114, 8]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(81⁴, 6562, F₈₁, 2, 3) (dual of [(6562, 2), 13120, 4]-NRT-code), using
- OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(81⁴, 6562, F₈₁, 3) (dual of [6562, 6558, 4]-code or 6562-cap in PG(3,81)), using
  - ovoid in PG(3,Â 81) [i]
linear OOA(81¹⁴, 3283, F₈₁, 2, 7) (dual of [(3283, 2), 6552, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(81¹⁴, 6566, F₈₁, 7) (dual of [6566, 6552, 8]-code), using
  - discarding factors / shortening the dual code based on linear OA(81¹⁴, 6567, F₈₁, 7) (dual of [6567, 6553, 8]-code), using
    - constructionÂ X applied to C([0,3]) âŠ‚ C([0,2]) [i] based on
      1. linear OA(81¹³, 6562, F₈₁, 7) (dual of [6562, 6549, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 81⁴âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
      2. linear OA(81⁹, 6562, F₈₁, 5) (dual of [6562, 6553, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 81⁴âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
      3. linear OA(81¹, 5, F₈₁, 1) (dual of [5, 4, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(81¹, s, F₈₁, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(81⁷¹, 4200867, F₈₁, 2, 14) (dual of [(4200867, 2), 8401663, 15]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(81⁷⁵, 4200867, F₈₁, 2, 15) (dual of [(4200867, 2), 8401659, 16]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs