MinT - Information on Result #1196128

Information on Result #1196128

Digital (57, 67, 2796200)-net over F₂₅, using net defined by OOA based on linear OOA(25⁶⁷, 2796200, F₂₅, 14, 10) (dual of [(2796200, 14), 39146733, 11]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(25⁶⁷, 8388601, F₂₅, 2, 10) (dual of [(8388601, 2), 16777135, 11]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25⁶⁷, 8388602, F₂₅, 2, 10) (dual of [(8388602, 2), 16777137, 11]-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(25⁴⁶, 4194301, F₂₅, 2, 10) (dual of [(4194301, 2), 8388556, 11]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(25⁴⁶, 8388602, F₂₅, 10) (dual of [8388602, 8388556, 11]-code), using
        discarding factors / shortening the dual code based on linear OA(25⁴⁶, large, F₂₅, 10) (dual of [large, large−46, 11]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 25⁵âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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 (124, 134, 5592400)-net over F₅	[i]		Trace Code for Nets