MinT - Information on Result #1197016

Information on Result #1197016

Digital (57, 84, 1204)-net over F₂₅, using net defined by OOA based on linear OOA(25⁸⁴, 1204, F₂₅, 27, 27) (dual of [(1204, 27), 32424, 28]-NRT-code), using

OOA 13-folding and stacking with additional row [i] based on linear OA(25⁸⁴, 15653, F₂₅, 27) (dual of [15653, 15569, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(25⁸⁴, 15654, F₂₅, 27) (dual of [15654, 15570, 28]-code), using
  - constructionÂ X applied to C_e(26) âŠ‚ C_e(18) [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(25⁵⁵, 15625, F₂₅, 19) (dual of [15625, 15570, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    3. linear OA(25⁸, 29, F₂₅, 7) (dual of [29, 21, 8]-code), using
      - constructionÂ X applied to AG(F,9P) âŠ‚ AG(F,10P) [i] based on
        linear OA(25⁷, 26, F₂₅, 7) (dual of [26, 19, 8]-code or 26-arc in PG(6,25)), using algebraic-geometric code AG(F,9P) with 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]
        linear OA(25⁵, 26, F₂₅, 5) (dual of [26, 21, 6]-code or 26-arc in PG(4,25)), using algebraic-geometric code AG(F,10P) with degPÂ =Â 2 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)
        linear OA(25¹, 3, F₂₅, 1) (dual of [3, 2, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(25¹, s, F₂₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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 (58, 84, 1204)-net over F₂₅	[i]	t-Expansion
2	Digital (58, 85, 1204)-net over F₂₅	[i]	Net Duplication
3	Digital (59, 86, 1204)-net over F₂₅	[i]
4	Digital (60, 87, 1204)-net over F₂₅	[i]
5	Digital (61, 88, 1204)-net over F₂₅	[i]
6	Digital (57, 83, 1204)-net over F₂₅	[i]	m-Reduction