MinT - Information on Result #893954

Information on Result #893954

Linear OOA(7⁶⁸, 5764812, F₇, 2, 9) (dual of [(5764812, 2), 11529556, 10]-NRT-code), using trace code based on linear OOA(49³⁴, 2882406, F₄₉, 2, 9) (dual of [(2882406, 2), 5764778, 10]-NRT-code), using

OOA 2-folding [i] based on linear OA(49³⁴, 5764812, F₄₉, 9) (dual of [5764812, 5764778, 10]-code), using
- constructionÂ X4 applied to C([0,4]) âŠ‚ C([0,3]) [i] based on
  1. 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]
  2. linear OA(49²⁵, 5764802, F₄₉, 7) (dual of [5764802, 5764777, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 5764802Â | 49⁸âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
  3. linear OA(49⁹, 10, F₄₉, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,49)), using
    - dual of repetition code with length 10 [i]
  4. linear OA(49¹, 10, F₄₉, 1) (dual of [10, 9, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(49¹, 49, F₄₉, 1) (dual of [49, 48, 2]-code), using
      - Reedâ€“Solomon code RS(48,49) [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(7⁶⁹, 5764812, F₇, 2, 9) (dual of [(5764812, 2), 11529555, 10]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(7⁶⁸, 2882406, F₇, 3, 9) (dual of [(2882406, 3), 8647150, 10]-NRT-code)	[i]	OOA Folding
3	Linear OOA(7⁶⁸, 2882405, F₇, 10, 9) (dual of [(2882405, 10), 28823982, 10]-NRT-code)	[i]	OOA Folding and Stacking with Additional Row