MinT - Information on Result #1196182

Information on Result #1196182

Digital (61, 72, 2796200)-net over F₂₅, using net defined by OOA based on linear OOA(25⁷², 2796200, F₂₅, 14, 11) (dual of [(2796200, 14), 39146728, 12]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(25⁷², 8388601, F₂₅, 2, 11) (dual of [(8388601, 2), 16777130, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25⁷², 8388602, F₂₅, 2, 11) (dual of [(8388602, 2), 16777132, 12]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(25²¹, 4194301, F₂₅, 2, 5) (dual of [(4194301, 2), 8388581, 6]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(25²¹, 8388602, F₂₅, 5) (dual of [8388602, 8388581, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(25²¹, large, F₂₅, 5) (dual of [large, large−21, 6]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 25¹⁰âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
    2. linear OOA(25⁵¹, 4194301, F₂₅, 2, 11) (dual of [(4194301, 2), 8388551, 12]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(25⁵¹, 8388602, F₂₅, 11) (dual of [8388602, 8388551, 12]-code), using
        discarding factors / shortening the dual code based on linear OA(25⁵¹, large, F₂₅, 11) (dual of [large, large−51, 12]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 25¹⁰âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (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 (133, 144, 5592400)-net over F₅	[i]		Trace Code for Nets