MinT - Information on Result #893987

Information on Result #893987

Linear OOA(7⁹⁸, 5764824, F₇, 2, 12) (dual of [(5764824, 2), 11529550, 13]-NRT-code), using trace code based on linear OOA(49⁴⁹, 2882412, F₄₉, 2, 12) (dual of [(2882412, 2), 5764775, 13]-NRT-code), using

OOA 2-folding [i] based on linear OA(49⁴⁹, 5764824, F₄₉, 12) (dual of [5764824, 5764775, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(49⁴⁹, 5764825, F₄₉, 12) (dual of [5764825, 5764776, 13]-code), using
  - constructionÂ X applied to C_e(11) âŠ‚ C_e(6) [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(49²⁵, 5764801, F₄₉, 7) (dual of [5764801, 5764776, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    3. linear OA(49⁴, 24, F₄₉, 4) (dual of [24, 20, 5]-code or 24-arc in PG(3,49)), using
      - discarding factors / shortening the dual code based on linear OA(49⁴, 49, F₄₉, 4) (dual of [49, 45, 5]-code or 49-arc in PG(3,49)), using
        Reedâ€“Solomon code RS(45,49) [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(7⁹⁹, 5764824, F₇, 2, 12) (dual of [(5764824, 2), 11529549, 13]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(7⁹⁸, 2882412, F₇, 3, 12) (dual of [(2882412, 3), 8647138, 13]-NRT-code)	[i]		OOA Folding