MinT - Information on Result #1204124

Information on Result #1204124

Digital (29, 56, 1261)-net over F₁₂₈, using net defined by OOA based on linear OOA(128⁵⁶, 1261, F₁₂₈, 27, 27) (dual of [(1261, 27), 33991, 28]-NRT-code), using

OOA 13-folding and stacking with additional row [i] based on linear OA(128⁵⁶, 16394, F₁₂₈, 27) (dual of [16394, 16338, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(128⁵⁶, 16396, F₁₂₈, 27) (dual of [16396, 16340, 28]-code), using
  - constructionÂ X applied to C([0,13]) âŠ‚ C([0,11]) [i] based on
    1. linear OA(128⁵³, 16385, F₁₂₈, 27) (dual of [16385, 16332, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
    2. linear OA(128⁴⁵, 16385, F₁₂₈, 23) (dual of [16385, 16340, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,11], and minimum distance dÂ â‰¥ |{−11,−10,…,11}|+1Â =Â 24 (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 (30, 56, 1261)-net over F₁₂₈	[i]	t-Expansion
2	Digital (30, 57, 1261)-net over F₁₂₈	[i]	Net Duplication
3	Digital (31, 58, 1261)-net over F₁₂₈	[i]
4	Digital (32, 59, 1261)-net over F₁₂₈	[i]
5	Digital (29, 55, 1261)-net over F₁₂₈	[i]	m-Reduction