MinT - Information on Result #1199236

Information on Result #1199236

Digital (39, 52, 174765)-net over F₃₂, using net defined by OOA based on linear OOA(32⁵², 174765, F₃₂, 13, 13) (dual of [(174765, 13), 2271893, 14]-NRT-code), using

OOA 6-folding and stacking with additional row [i] based on linear OA(32⁵², 1048591, F₃₂, 13) (dual of [1048591, 1048539, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(32⁵², 1048596, F₃₂, 13) (dual of [1048596, 1048544, 14]-code), using
  - constructionÂ X applied to C([0,6]) âŠ‚ C([0,4]) [i] based on
    1. linear OA(32⁴⁹, 1048577, F₃₂, 13) (dual of [1048577, 1048528, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 32⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
    2. linear OA(32³³, 1048577, F₃₂, 9) (dual of [1048577, 1048544, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 32⁸âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
    3. linear OA(32³, 19, F₃₂, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,32) or 19-cap in PG(2,32)), using
      - discarding factors / shortening the dual code based on linear OA(32³, 32, F₃₂, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
        Reedâ€“Solomon code RS(29,32) [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 (97, 110, 5592480)-net over F₃₂	[i]		Generalized (u,Â u+v)-Construction for Nets