MinT - Information on Result #1197146

Information on Result #1197146

Digital (67, 100, 978)-net over F₂₅, using net defined by OOA based on linear OOA(25¹⁰⁰, 978, F₂₅, 33, 33) (dual of [(978, 33), 32174, 34]-NRT-code), using

OOA 16-folding and stacking with additional row [i] based on linear OA(25¹⁰⁰, 15649, F₂₅, 33) (dual of [15649, 15549, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(25¹⁰⁰, 15651, F₂₅, 33) (dual of [15651, 15551, 34]-code), using
  - constructionÂ X applied to C_e(32) âŠ‚ C_e(25) [i] based on
    1. linear OA(25⁹⁴, 15625, F₂₅, 33) (dual of [15625, 15531, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
    2. linear OA(25⁷³, 15625, F₂₅, 26) (dual of [15625, 15552, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
    3. linear OA(25⁶, 26, F₂₅, 6) (dual of [26, 20, 7]-code or 26-arc in PG(5,25)), using
      - extended Reedâ€“Solomon code RS_e(20,25) [i]
      - algebraic-geometric code AG(F, Q+8P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using the rational function field F₂₅(x) [i]
      - algebraic-geometric code AG(F, Q+5P) with degQ = 4 and degPÂ =Â 3 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)

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 (68, 100, 978)-net over F₂₅	[i]	t-Expansion
2	Digital (68, 101, 978)-net over F₂₅	[i]	Net Duplication
3	Digital (69, 102, 978)-net over F₂₅	[i]
4	Digital (70, 103, 978)-net over F₂₅	[i]
5	Digital (71, 104, 978)-net over F₂₅	[i]
6	Digital (72, 105, 978)-net over F₂₅	[i]
7	Digital (73, 106, 978)-net over F₂₅	[i]
8	Digital (67, 99, 978)-net over F₂₅	[i]	m-Reduction