MinT - Information on Result #1199974

Information on Result #1199974

Digital (52, 77, 2732)-net over F₃₂, using net defined by OOA based on linear OOA(32⁷⁷, 2732, F₃₂, 25, 25) (dual of [(2732, 25), 68223, 26]-NRT-code), using

OOA 12-folding and stacking with additional row [i] based on linear OA(32⁷⁷, 32785, F₃₂, 25) (dual of [32785, 32708, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(32⁷⁷, 32787, F₃₂, 25) (dual of [32787, 32710, 26]-code), using
  - constructionÂ X applied to C_e(24) âŠ‚ C_e(19) [i] based on
    1. linear OA(32⁷³, 32768, F₃₂, 25) (dual of [32768, 32695, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
    2. linear OA(32⁵⁸, 32768, F₃₂, 20) (dual of [32768, 32710, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
    3. linear OA(32⁴, 19, F₃₂, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,32)), using
      - discarding factors / shortening the dual code based on linear OA(32⁴, 32, F₃₂, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
        Reedâ€“Solomon code RS(28,32) [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		Method
1	Digital (53, 78, 2732)-net over F₃₂	[i]	Net Duplication
2	Digital (54, 79, 2732)-net over F₃₂	[i]	Net Duplication
3	Digital (52, 76, 2732)-net over F₃₂	[i]	m-Reduction