MinT - Information on Result #1195986

Information on Result #1195986

Digital (37, 45, 2097638)-net over F₂₅, using net defined by OOA based on linear OOA(25⁴⁵, 2097638, F₂₅, 10, 8) (dual of [(2097638, 10), 20976335, 9]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(25⁴⁵, 4195277, F₂₅, 2, 8) (dual of [(4195277, 2), 8390509, 9]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(25⁹, 976, F₂₅, 2, 4) (dual of [(976, 2), 1943, 5]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(25⁹, 1952, F₂₅, 4) (dual of [1952, 1943, 5]-code), using
      - discarding factors / shortening the dual code based on linear OA(25⁹, 1953, F₂₅, 4) (dual of [1953, 1944, 5]-code), using
        the BCH-code C(I) with length 1953Â | 25³âˆ’1, defining interval IÂ =Â {1,9,17,25}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
  2. linear OOA(25³⁶, 4194301, F₂₅, 2, 8) (dual of [(4194301, 2), 8388566, 9]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(25³⁶, 8388602, F₂₅, 8) (dual of [8388602, 8388566, 9]-code), using
      - discarding factors / shortening the dual code based on linear OA(25³⁶, large, F₂₅, 8) (dual of [large, large−36, 9]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 25⁵âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [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 (82, 90, 4195276)-net over F₅	[i]		Trace Code for Nets