MinT - Information on Result #1199812

Information on Result #1199812

Digital (63, 84, 104859)-net over F₃₂, using net defined by OOA based on linear OOA(32⁸⁴, 104859, F₃₂, 21, 21) (dual of [(104859, 21), 2201955, 22]-NRT-code), using

OOA 10-folding and stacking with additional row [i] based on linear OA(32⁸⁴, 1048591, F₃₂, 21) (dual of [1048591, 1048507, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(32⁸⁴, 1048596, F₃₂, 21) (dual of [1048596, 1048512, 22]-code), using
  - constructionÂ X applied to C([0,10]) âŠ‚ C([0,8]) [i] based on
    1. linear OA(32⁸¹, 1048577, F₃₂, 21) (dual of [1048577, 1048496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 32⁸âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
    2. linear OA(32⁶⁵, 1048577, F₃₂, 17) (dual of [1048577, 1048512, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 32⁸âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (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 (64, 85, 104859)-net over F₃₂	[i]		Net Duplication