MinT - Information on Result #893985

Information on Result #893985

Linear OOA(7⁹⁶, 5764820, F₇, 2, 12) (dual of [(5764820, 2), 11529544, 13]-NRT-code), using trace code based on linear OOA(49⁴⁸, 2882410, F₄₉, 2, 12) (dual of [(2882410, 2), 5764772, 13]-NRT-code), using

OOA 2-folding [i] based on linear OA(49⁴⁸, 5764820, F₄₉, 12) (dual of [5764820, 5764772, 13]-code), using
- constructionÂ X applied to C_e(11) âŠ‚ C_e(7) [i] based on
  1. linear OA(49⁴⁵, 5764801, F₄₉, 12) (dual of [5764801, 5764756, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [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(49³, 19, F₄₉, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,49) or 19-cap in PG(2,49)), using
    - discarding factors / shortening the dual code based on linear OA(49³, 49, F₄₉, 3) (dual of [49, 46, 4]-code or 49-arc in PG(2,49) or 49-cap in PG(2,49)), using
      - Reedâ€“Solomon code RS(46,49) [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(7⁹⁷, 5764820, F₇, 2, 12) (dual of [(5764820, 2), 11529543, 13]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(7⁹⁶, 2882410, F₇, 3, 12) (dual of [(2882410, 3), 8647134, 13]-NRT-code)	[i]	OOA Folding
3	Linear OOA(7⁹⁶, 1921606, F₇, 14, 12) (dual of [(1921606, 14), 26902388, 13]-NRT-code)	[i]	OOA Folding and Stacking with Additional Row