MinT - Information on Result #876987

Information on Result #876987

Linear OOA(81⁷⁶, 265728, F₈₁, 2, 25) (dual of [(265728, 2), 531380, 26]-NRT-code), using OOA 2-folding based on linear OA(81⁷⁶, 531456, F₈₁, 25) (dual of [531456, 531380, 26]-code), using

discarding factors / shortening the dual code based on linear OA(81⁷⁶, 531457, F₈₁, 25) (dual of [531457, 531381, 26]-code), using
- constructionÂ X applied to C([0,12]) âŠ‚ C([0,10]) [i] based on
  1. linear OA(81⁷³, 531442, F₈₁, 25) (dual of [531442, 531369, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 81⁶âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
  2. linear OA(81⁶¹, 531442, F₈₁, 21) (dual of [531442, 531381, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 81⁶âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (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(81⁷⁶, 265728, F₈₁, 3, 25) (dual of [(265728, 3), 797108, 26]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(81⁷⁶, 265728, F₈₁, 4, 25) (dual of [(265728, 4), 1062836, 26]-NRT-code)	[i]
3	Digital (51, 76, 265728)-net over F₈₁	[i]