MinT - Information on Result #893991

Information on Result #893991

Linear OOA(7¹⁰⁰, 5764810, F₇, 2, 13) (dual of [(5764810, 2), 11529520, 14]-NRT-code), using trace code based on linear OOA(49⁵⁰, 2882405, F₄₉, 2, 13) (dual of [(2882405, 2), 5764760, 14]-NRT-code), using

OOA 2-folding [i] based on linear OA(49⁵⁰, 5764810, F₄₉, 13) (dual of [5764810, 5764760, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(49⁵⁰, 5764811, F₄₉, 13) (dual of [5764811, 5764761, 14]-code), using
  - constructionÂ X applied to C([0,6]) âŠ‚ C([0,5]) [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(49⁴¹, 5764802, F₄₉, 11) (dual of [5764802, 5764761, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 5764802Â | 49⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]
    3. linear OA(49¹, 9, F₄₉, 1) (dual of [9, 8, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(49¹, s, F₄₉, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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(7¹⁰¹, 5764810, F₇, 2, 13) (dual of [(5764810, 2), 11529519, 14]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(7¹⁰⁰, 2882405, F₇, 3, 13) (dual of [(2882405, 3), 8647115, 14]-NRT-code)	[i]	OOA Folding
3	Linear OOA(7¹⁰⁰, 1921603, F₇, 14, 13) (dual of [(1921603, 14), 26902342, 14]-NRT-code)	[i]	OOA Folding and Stacking with Additional Row