MinT - Information on Result #1197014

Information on Result #1197014

Digital (53, 80, 1203)-net over F₂₅, using net defined by OOA based on linear OOA(25⁸⁰, 1203, F₂₅, 27, 27) (dual of [(1203, 27), 32401, 28]-NRT-code), using

OOA 13-folding and stacking with additional row [i] based on linear OA(25⁸⁰, 15640, F₂₅, 27) (dual of [15640, 15560, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(25⁸⁰, 15641, F₂₅, 27) (dual of [15641, 15561, 28]-code), using
  - constructionÂ X applied to C_e(26) âŠ‚ C_e(21) [i] based on
    1. linear OA(25⁷⁶, 15625, F₂₅, 27) (dual of [15625, 15549, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
    2. linear OA(25⁶⁴, 15625, F₂₅, 22) (dual of [15625, 15561, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
    3. linear OA(25⁴, 16, F₂₅, 4) (dual of [16, 12, 5]-code or 16-arc in PG(3,25)), using
      - discarding factors / shortening the dual code based on linear OA(25⁴, 25, F₂₅, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
        Reedâ€“Solomon code RS(21,25) [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 (54, 80, 1203)-net over F₂₅	[i]	t-Expansion
2	Digital (54, 81, 1203)-net over F₂₅	[i]	Net Duplication
3	Digital (55, 82, 1203)-net over F₂₅	[i]
4	Digital (56, 83, 1203)-net over F₂₅	[i]
5	Digital (53, 79, 1203)-net over F₂₅	[i]	m-Reduction
6	Digital (70, 97, 1269)-net over F₂₅	[i]	(u,Â u+v)-Construction for Nets