MinT - Information on Result #877092

Information on Result #877092

Linear OOA(81⁸², 265728, F₈₁, 2, 27) (dual of [(265728, 2), 531374, 28]-NRT-code), using OOA 2-folding based on linear OA(81⁸², 531456, F₈₁, 27) (dual of [531456, 531374, 28]-code), using

discarding factors / shortening the dual code based on linear OA(81⁸², 531457, F₈₁, 27) (dual of [531457, 531375, 28]-code), using
- constructionÂ X applied to C([0,13]) âŠ‚ C([0,11]) [i] based on
  1. linear OA(81⁷⁹, 531442, F₈₁, 27) (dual of [531442, 531363, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 81⁶âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
  2. linear OA(81⁶⁷, 531442, F₈₁, 23) (dual of [531442, 531375, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 81⁶âˆ’1, defining interval IÂ =Â [0,11], and minimum distance dÂ â‰¥ |{−11,−10,…,11}|+1Â =Â 24 (BCH-bound) [i]
  3. linear OA(81³, 15, F₈₁, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,81) or 15-cap in PG(2,81)), using
    - discarding factors / shortening the dual code based on linear OA(81³, 81, F₈₁, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
      - Reedâ€“Solomon code RS(78,81) [i]

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(81⁸², 265728, F₈₁, 3, 27) (dual of [(265728, 3), 797102, 28]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(81⁸², 265728, F₈₁, 4, 27) (dual of [(265728, 4), 1062830, 28]-NRT-code)	[i]
3	Digital (55, 82, 265728)-net over F₈₁	[i]