MinT - Information on Result #893996

Information on Result #893996

Linear OOA(7¹⁰⁴, 5764820, F₇, 2, 13) (dual of [(5764820, 2), 11529536, 14]-NRT-code), using trace code based on linear OOA(49⁵², 2882410, F₄₉, 2, 13) (dual of [(2882410, 2), 5764768, 14]-NRT-code), using

OOA 2-folding [i] based on linear OA(49⁵², 5764820, F₄₉, 13) (dual of [5764820, 5764768, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(49⁵², 5764821, F₄₉, 13) (dual of [5764821, 5764769, 14]-code), using
  - constructionÂ X applied to C([0,6]) âŠ‚ C([0,4]) [i] based on
    1. linear OA(49⁴⁹, 5764802, F₄₉, 13) (dual of [5764802, 5764753, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 5764802Â | 49⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
    2. linear OA(49³³, 5764802, F₄₉, 9) (dual of [5764802, 5764769, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 5764802Â | 49⁸âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
    3. linear OA(49³, 19, F₄₉, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,49) or 19-cap in PG(2,49)), using
      - discarding factors / shortening the dual code based on linear OA(49³, 49, F₄₉, 3) (dual of [49, 46, 4]-code or 49-arc in PG(2,49) or 49-cap in PG(2,49)), using
        Reedâ€“Solomon code RS(46,49) [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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(7¹⁰⁵, 5764820, F₇, 2, 13) (dual of [(5764820, 2), 11529535, 14]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(7¹⁰⁴, 2882410, F₇, 3, 13) (dual of [(2882410, 3), 8647126, 14]-NRT-code)	[i]	OOA Folding
3	Linear OOA(7¹⁰⁴, 1921606, F₇, 14, 13) (dual of [(1921606, 14), 26902380, 14]-NRT-code)	[i]	OOA Folding and Stacking with Additional Row