MinT - Information on Result #893994

Information on Result #893994

Linear OOA(7¹⁰², 5764814, F₇, 2, 13) (dual of [(5764814, 2), 11529526, 14]-NRT-code), using trace code based on linear OOA(49⁵¹, 2882407, F₄₉, 2, 13) (dual of [(2882407, 2), 5764763, 14]-NRT-code), using

OOA 2-folding [i] based on linear OA(49⁵¹, 5764814, F₄₉, 13) (dual of [5764814, 5764763, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(49⁵¹, 5764815, F₄₉, 13) (dual of [5764815, 5764764, 14]-code), using
  - constructionÂ X applied to C_e(12) âŠ‚ C_e(9) [i] based on
    1. linear OA(49⁴⁹, 5764801, F₄₉, 13) (dual of [5764801, 5764752, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    2. linear OA(49³⁷, 5764801, F₄₉, 10) (dual of [5764801, 5764764, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
    3. linear OA(49², 14, F₄₉, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,49)), using
      - discarding factors / shortening the dual code based on linear OA(49², 49, F₄₉, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), using
        Reedâ€“Solomon code RS(47,49) [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(7¹⁰³, 5764814, F₇, 2, 13) (dual of [(5764814, 2), 11529525, 14]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(7¹⁰², 2882407, F₇, 3, 13) (dual of [(2882407, 3), 8647119, 14]-NRT-code)	[i]	OOA Folding
3	Linear OOA(7¹⁰², 1921604, F₇, 14, 13) (dual of [(1921604, 14), 26902354, 14]-NRT-code)	[i]	OOA Folding and Stacking with Additional Row