MinT - Information on Result #1196226

Information on Result #1196226

Digital (51, 63, 1398109)-net over F₂₅, using net defined by OOA based on linear OOA(25⁶³, 1398109, F₂₅, 14, 12) (dual of [(1398109, 14), 19573463, 13]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(25⁶³, 4194328, F₂₅, 2, 12) (dual of [(4194328, 2), 8388593, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(25⁷, 27, F₂₅, 2, 6) (dual of [(27, 2), 47, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 7, 27)-net over F₂₅, using
      - net from sequence [i] based on digital (1, 26)-sequence over F₂₅, using
        Niederreiter sequence [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 (114, 126, 2796218)-net over F₅	[i]		Trace Code for Nets