MinT - Information on Result #1198662

Information on Result #1198662

Digital (64, 97, 1231)-net over F₂₇, using net defined by OOA based on linear OOA(27⁹⁷, 1231, F₂₇, 33, 33) (dual of [(1231, 33), 40526, 34]-NRT-code), using

OOA 16-folding and stacking with additional row [i] based on linear OA(27⁹⁷, 19697, F₂₇, 33) (dual of [19697, 19600, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(27⁹⁷, 19698, F₂₇, 33) (dual of [19698, 19601, 34]-code), using
  - constructionÂ X applied to C_e(32) âŠ‚ C_e(28) [i] based on
    1. linear OA(27⁹⁴, 19683, F₂₇, 33) (dual of [19683, 19589, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
    2. linear OA(27⁸², 19683, F₂₇, 29) (dual of [19683, 19601, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
    3. linear OA(27³, 15, F₂₇, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,27) or 15-cap in PG(2,27)), using
      - discarding factors / shortening the dual code based on linear OA(27³, 27, F₂₇, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), using
        Reedâ€“Solomon code RS(24,27) [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 (65, 97, 1231)-net over F₂₇	[i]	t-Expansion
2	Digital (65, 98, 1231)-net over F₂₇	[i]	Net Duplication
3	Digital (66, 99, 1231)-net over F₂₇	[i]
4	Digital (67, 100, 1231)-net over F₂₇	[i]
5	Digital (68, 101, 1231)-net over F₂₇	[i]
6	Digital (69, 102, 1231)-net over F₂₇	[i]
7	Digital (64, 96, 1231)-net over F₂₇	[i]	m-Reduction