MinT - Information on Result #1198992

Information on Result #1198992

Digital (50, 59, 4194301)-net over F₃₂, using net defined by OOA based on linear OOA(32⁵⁹, 4194301, F₃₂, 10, 9) (dual of [(4194301, 10), 41942951, 10]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(32⁵⁹, large, F₃₂, 2, 9), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(32⁵⁷, 8388602, F₃₂, 2, 9) (dual of [(8388602, 2), 16777147, 10]-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(32⁴¹, 4194301, F₃₂, 2, 9) (dual of [(4194301, 2), 8388561, 10]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(32⁴¹, 8388602, F₃₂, 9) (dual of [8388602, 8388561, 10]-code), using
        discarding factors / shortening the dual code based on linear OA(32⁴¹, large, F₃₂, 9) (dual of [large, large−41, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 33554433Â | 32¹⁰âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (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 (66, 75, 8388602)-net over F₃₂	[i]		(u,Â u+v)-Construction for Nets