MinT - Information on Result #893956

Information on Result #893956

Linear OOA(7⁷⁰, 5764814, F₇, 2, 9) (dual of [(5764814, 2), 11529558, 10]-NRT-code), using trace code based on linear OOA(49³⁵, 2882407, F₄₉, 2, 9) (dual of [(2882407, 2), 5764779, 10]-NRT-code), using

OOA 2-folding [i] based on linear OA(49³⁵, 5764814, F₄₉, 9) (dual of [5764814, 5764779, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(49³⁵, 5764815, F₄₉, 9) (dual of [5764815, 5764780, 10]-code), using
  - constructionÂ X applied to C_e(8) âŠ‚ C_e(5) [i] based on
    1. linear OA(49³³, 5764801, F₄₉, 9) (dual of [5764801, 5764768, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
    2. linear OA(49²¹, 5764801, F₄₉, 6) (dual of [5764801, 5764780, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [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		This result only	Method
1	Linear OOA(7⁷⁰, 2882407, F₇, 3, 9) (dual of [(2882407, 3), 8647151, 10]-NRT-code)	[i]		OOA Folding
2	Linear OOA(7⁷⁰, 2882406, F₇, 10, 9) (dual of [(2882406, 10), 28823990, 10]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row