MinT - Information on Result #893973

Information on Result #893973

Linear OOA(7⁸⁶, 5764814, F₇, 2, 11) (dual of [(5764814, 2), 11529542, 12]-NRT-code), using trace code based on linear OOA(49⁴³, 2882407, F₄₉, 2, 11) (dual of [(2882407, 2), 5764771, 12]-NRT-code), using

OOA 2-folding [i] based on linear OA(49⁴³, 5764814, F₄₉, 11) (dual of [5764814, 5764771, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(49⁴³, 5764815, F₄₉, 11) (dual of [5764815, 5764772, 12]-code), using
  - constructionÂ X applied to C_e(10) âŠ‚ C_e(7) [i] based on
    1. linear OA(49⁴¹, 5764801, F₄₉, 11) (dual of [5764801, 5764760, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
    2. linear OA(49²⁹, 5764801, F₄₉, 8) (dual of [5764801, 5764772, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [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(7⁸⁷, 5764814, F₇, 2, 11) (dual of [(5764814, 2), 11529541, 12]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(7⁸⁶, 2882407, F₇, 3, 11) (dual of [(2882407, 3), 8647135, 12]-NRT-code)	[i]	OOA Folding
3	Linear OOA(7⁸⁶, 1921604, F₇, 14, 11) (dual of [(1921604, 14), 26902370, 12]-NRT-code)	[i]	OOA Folding and Stacking with Additional Row