MinT - Information on Result #1203904

Information on Result #1203904

Digital (25, 46, 1640)-net over F₁₂₈, using net defined by OOA based on linear OOA(128⁴⁶, 1640, F₁₂₈, 21, 21) (dual of [(1640, 21), 34394, 22]-NRT-code), using

OOA 10-folding and stacking with additional row [i] based on linear OA(128⁴⁶, 16401, F₁₂₈, 21) (dual of [16401, 16355, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(128⁴⁶, 16402, F₁₂₈, 21) (dual of [16402, 16356, 22]-code), using
  - constructionÂ X applied to C([0,10]) âŠ‚ C([0,7]) [i] based on
    1. 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]
    2. linear OA(128²⁹, 16385, F₁₂₈, 15) (dual of [16385, 16356, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
    3. linear OA(128⁵, 17, F₁₂₈, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,128)), using
      - discarding factors / shortening the dual code based on linear OA(128⁵, 128, F₁₂₈, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
        Reedâ€“Solomon code RS(123,128) [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 (26, 46, 1640)-net over F₁₂₈	[i]	t-Expansion
2	Digital (26, 47, 1640)-net over F₁₂₈	[i]	Net Duplication
3	Digital (27, 48, 1640)-net over F₁₂₈	[i]
4	Digital (28, 49, 1640)-net over F₁₂₈	[i]
5	Digital (25, 45, 1640)-net over F₁₂₈	[i]	m-Reduction