MinT - Information on Result #1204060

Information on Result #1204060

Digital (27, 52, 1366)-net over F₁₂₈, using net defined by OOA based on linear OOA(128⁵², 1366, F₁₂₈, 25, 25) (dual of [(1366, 25), 34098, 26]-NRT-code), using

OOA 12-folding and stacking with additional row [i] based on linear OA(128⁵², 16393, F₁₂₈, 25) (dual of [16393, 16341, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(128⁵², 16396, F₁₂₈, 25) (dual of [16396, 16344, 26]-code), using
  - constructionÂ X applied to C([0,12]) âŠ‚ C([0,10]) [i] based on
    1. linear OA(128⁴⁹, 16385, F₁₂₈, 25) (dual of [16385, 16336, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
    2. linear OA(128⁴¹, 16385, F₁₂₈, 21) (dual of [16385, 16344, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
    3. linear OA(128³, 11, F₁₂₈, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,128) or 11-cap in PG(2,128)), using
      - discarding factors / shortening the dual code based on linear OA(128³, 128, F₁₂₈, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
        Reedâ€“Solomon code RS(125,128) [i]

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Digital (28, 52, 1366)-net over F₁₂₈	[i]	t-Expansion
2	Digital (28, 53, 1366)-net over F₁₂₈	[i]	Net Duplication
3	Digital (29, 54, 1366)-net over F₁₂₈	[i]
4	Digital (30, 55, 1366)-net over F₁₂₈	[i]
5	Digital (27, 51, 1366)-net over F₁₂₈	[i]	m-Reduction