MinT - Information on Result #1196970

Information on Result #1196970

Digital (74, 99, 32553)-net over F₂₅, using net defined by OOA based on linear OOA(25⁹⁹, 32553, F₂₅, 25, 25) (dual of [(32553, 25), 813726, 26]-NRT-code), using

OOA 12-folding and stacking with additional row [i] based on linear OA(25⁹⁹, 390637, F₂₅, 25) (dual of [390637, 390538, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(25⁹⁹, 390639, F₂₅, 25) (dual of [390639, 390540, 26]-code), using
  - 1 times truncation [i] based on linear OA(25¹⁰⁰, 390640, F₂₅, 26) (dual of [390640, 390540, 27]-code), using
    - constructionÂ X applied to C_e(25) âŠ‚ C_e(21) [i] based on
      1. linear OA(25⁹⁷, 390625, F₂₅, 26) (dual of [390625, 390528, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
      2. linear OA(25⁸⁵, 390625, F₂₅, 22) (dual of [390625, 390540, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      3. linear OA(25³, 15, F₂₅, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,25) or 15-cap in PG(2,25)), using
        discarding factors / shortening the dual code based on linear OA(25³, 25, F₂₅, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
        Reedâ€“Solomon code RS(22,25) [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		This result only	Method
1	Digital (75, 100, 32553)-net over F₂₅	[i]		Net Duplication