MinT - Information on Result #1196224

Information on Result #1196224

Digital (50, 62, 1398108)-net over F₂₅, using net defined by OOA based on linear OOA(25⁶², 1398108, F₂₅, 14, 12) (dual of [(1398108, 14), 19573450, 13]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(25⁶², 4194325, F₂₅, 2, 12) (dual of [(4194325, 2), 8388588, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25⁶², 4194327, F₂₅, 2, 12) (dual of [(4194327, 2), 8388592, 13]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(25⁶, 26, F₂₅, 2, 6) (dual of [(26, 2), 46, 7]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;46,25) [i]
    2. linear OOA(25⁵⁶, 4194301, F₂₅, 2, 12) (dual of [(4194301, 2), 8388546, 13]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(25⁵⁶, 8388602, F₂₅, 12) (dual of [8388602, 8388546, 13]-code), using
        discarding factors / shortening the dual code based on linear OA(25⁵⁶, large, F₂₅, 12) (dual of [large, large−56, 13]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 25⁵âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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 (112, 124, 2796216)-net over F₅	[i]		Trace Code for Nets