MinT - Information on Result #893999

Information on Result #893999

Linear OOA(7¹⁰⁶, 5764804, F₇, 2, 14) (dual of [(5764804, 2), 11529502, 15]-NRT-code), using trace code based on linear OOA(49⁵³, 2882402, F₄₉, 2, 14) (dual of [(2882402, 2), 5764751, 15]-NRT-code), using

OOA 2-folding [i] based on linear OA(49⁵³, 5764804, F₄₉, 14) (dual of [5764804, 5764751, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(49⁵³, 5764805, F₄₉, 14) (dual of [5764805, 5764752, 15]-code), using
  - constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
    1. linear OA(49⁵³, 5764801, F₄₉, 14) (dual of [5764801, 5764748, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
    2. 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]
    3. linear OA(49⁰, 4, F₄₉, 0) (dual of [4, 4, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(49⁰, s, F₄₉, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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(7¹⁰⁷, 5764804, F₇, 2, 14) (dual of [(5764804, 2), 11529501, 15]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(7¹⁰⁶, 2882402, F₇, 3, 14) (dual of [(2882402, 3), 8647100, 15]-NRT-code)	[i]	OOA Folding
3	Linear OOA(7¹⁰⁶, 1441200, F₇, 18, 14) (dual of [(1441200, 18), 25941494, 15]-NRT-code)	[i]	OOA Folding and Stacking with Additional Row