MinT - Information on Result #1198916

Information on Result #1198916

Digital (46, 54, 4194301)-net over F₃₂, using net defined by OOA based on linear OOA(32⁵⁴, 4194301, F₃₂, 10, 8) (dual of [(4194301, 10), 41942956, 9]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(32⁵⁴, large, F₃₂, 2, 8), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(32⁵², 8388602, F₃₂, 2, 8) (dual of [(8388602, 2), 16777152, 9]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(32¹⁶, 4194301, F₃₂, 2, 4) (dual of [(4194301, 2), 8388586, 5]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(32¹⁶, 8388602, F₃₂, 4) (dual of [8388602, 8388586, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(32¹⁶, large, F₃₂, 4) (dual of [large, large−16, 5]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 33554431Â = 32⁵âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
    2. linear OOA(32³⁶, 4194301, F₃₂, 2, 8) (dual of [(4194301, 2), 8388566, 9]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(32³⁶, 8388602, F₃₂, 8) (dual of [8388602, 8388566, 9]-code), using
        discarding factors / shortening the dual code based on linear OA(32³⁶, large, F₃₂, 8) (dual of [large, large−36, 9]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 33554431Â = 32⁵âˆ’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 (62, 70, 8388602)-net over F₃₂	[i]		(u,Â u+v)-Construction for Nets