MinT - Information on Result #1196624

Information on Result #1196624

Digital (51, 69, 43403)-net over F₂₅, using net defined by OOA based on linear OOA(25⁶⁹, 43403, F₂₅, 18, 18) (dual of [(43403, 18), 781185, 19]-NRT-code), using

OA 9-folding and stacking [i] based on linear OA(25⁶⁹, 390627, F₂₅, 18) (dual of [390627, 390558, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(25⁶⁹, 390629, F₂₅, 18) (dual of [390629, 390560, 19]-code), using
  - constructionÂ X applied to C_e(17) âŠ‚ C_e(16) [i] based on
    1. linear OA(25⁶⁹, 390625, F₂₅, 18) (dual of [390625, 390556, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
    2. linear OA(25⁶⁵, 390625, F₂₅, 17) (dual of [390625, 390560, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    3. linear OA(25⁰, 4, F₂₅, 0) (dual of [4, 4, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(25⁰, s, F₂₅, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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 (52, 70, 43403)-net over F₂₅	[i]	Net Duplication
2	Digital (60, 78, 43429)-net over F₂₅	[i]	(u,Â u+v)-Construction for Nets
3	Digital (61, 79, 43430)-net over F₂₅	[i]
4	Digital (62, 80, 43431)-net over F₂₅	[i]
5	Digital (63, 81, 43455)-net over F₂₅	[i]
6	Digital (64, 82, 43469)-net over F₂₅	[i]
7	Digital (67, 85, 43481)-net over F₂₅	[i]