MinT - Information on Result #893998

Information on Result #893998

Linear OOA(7¹⁰⁶, 5764824, F₇, 2, 13) (dual of [(5764824, 2), 11529542, 14]-NRT-code), using trace code based on linear OOA(49⁵³, 2882412, F₄₉, 2, 13) (dual of [(2882412, 2), 5764771, 14]-NRT-code), using

OOA 2-folding [i] based on linear OA(49⁵³, 5764824, F₄₉, 13) (dual of [5764824, 5764771, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(49⁵³, 5764825, F₄₉, 13) (dual of [5764825, 5764772, 14]-code), using
  - constructionÂ X applied to C_e(12) âŠ‚ C_e(7) [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(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(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(7¹⁰⁷, 5764824, F₇, 2, 13) (dual of [(5764824, 2), 11529541, 14]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(7¹⁰⁶, 2882412, F₇, 3, 13) (dual of [(2882412, 3), 8647130, 14]-NRT-code)	[i]		OOA Folding