MinT - Information on Result #1198452

Information on Result #1198452

Digital (53, 78, 1642)-net over F₂₇, using net defined by OOA based on linear OOA(27⁷⁸, 1642, F₂₇, 25, 25) (dual of [(1642, 25), 40972, 26]-NRT-code), using

OOA 12-folding and stacking with additional row [i] based on linear OA(27⁷⁸, 19705, F₂₇, 25) (dual of [19705, 19627, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(27⁷⁸, 19707, F₂₇, 25) (dual of [19707, 19629, 26]-code), using
  - constructionÂ X applied to C([0,12]) âŠ‚ C([0,9]) [i] based on
    1. linear OA(27⁷³, 19684, F₂₇, 25) (dual of [19684, 19611, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684Â | 27⁶âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
    2. linear OA(27⁵⁵, 19684, F₂₇, 19) (dual of [19684, 19629, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684Â | 27⁶âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
    3. linear OA(27⁵, 23, F₂₇, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,27)), using
      - discarding factors / shortening the dual code based on linear OA(27⁵, 27, F₂₇, 5) (dual of [27, 22, 6]-code or 27-arc in PG(4,27)), using
        Reedâ€“Solomon code RS(22,27) [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 (54, 78, 1642)-net over F₂₇	[i]	t-Expansion
2	Digital (54, 79, 1642)-net over F₂₇	[i]	Net Duplication
3	Digital (55, 80, 1642)-net over F₂₇	[i]
4	Digital (56, 81, 1642)-net over F₂₇	[i]
5	Digital (53, 77, 1642)-net over F₂₇	[i]	m-Reduction