MinT - Information on Result #1196312

Information on Result #1196312

Digital (58, 71, 1398122)-net over F₂₅, using net defined by OOA based on linear OOA(25⁷¹, 1398122, F₂₅, 14, 13) (dual of [(1398122, 14), 19573637, 14]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(25⁷¹, 4194367, F₂₅, 2, 13) (dual of [(4194367, 2), 8388663, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(25¹⁰, 66, F₂₅, 2, 6) (dual of [(66, 2), 122, 7]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,125P) [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]
  2. linear OOA(25⁶¹, 4194301, F₂₅, 2, 13) (dual of [(4194301, 2), 8388541, 14]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(25⁶¹, 8388602, F₂₅, 13) (dual of [8388602, 8388541, 14]-code), using
      - discarding factors / shortening the dual code based on linear OA(25⁶¹, large, F₂₅, 13) (dual of [large, large−61, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 25¹⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [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 (129, 142, 2796244)-net over F₅	[i]		Trace Code for Nets