MinT - Information on Result #1060095

Information on Result #1060095

Linear OOA(3¹⁸⁴, 2391488, F₃, 4, 15) (dual of [(2391488, 4), 9565768, 16]-NRT-code), using OOA 2-folding based on linear OOA(3¹⁸⁴, 4782976, F₃, 2, 15) (dual of [(4782976, 2), 9565768, 16]-NRT-code), using

trace code [i] based on linear OOA(9⁹², 2391488, F₉, 2, 15) (dual of [(2391488, 2), 4782884, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(9⁹², 4782976, F₉, 15) (dual of [4782976, 4782884, 16]-code), using
  - constructionÂ X applied to C_e(14) âŠ‚ C_e(13) [i] based on
    1. linear OA(9⁹², 4782969, F₉, 15) (dual of [4782969, 4782877, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
    2. linear OA(9⁸⁵, 4782969, F₉, 14) (dual of [4782969, 4782884, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
    3. linear OA(9⁰, 7, F₉, 0) (dual of [7, 7, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 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(3¹⁸⁵, 2391488, F₃, 4, 15) (dual of [(2391488, 4), 9565767, 16]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3¹⁹⁵, 2391503, F₃, 4, 15) (dual of [(2391503, 4), 9565817, 16]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(3¹⁹⁶, 2391508, F₃, 4, 15) (dual of [(2391508, 4), 9565836, 16]-NRT-code)	[i]
4	Linear OOA(3¹⁹⁷, 2391514, F₃, 4, 15) (dual of [(2391514, 4), 9565859, 16]-NRT-code)	[i]
5	Linear OOA(3¹⁹⁸, 2391522, F₃, 4, 15) (dual of [(2391522, 4), 9565890, 16]-NRT-code)	[i]
6	Linear OOA(3²⁰¹, 2391528, F₃, 4, 15) (dual of [(2391528, 4), 9565911, 16]-NRT-code)	[i]
7	Linear OOA(3²⁰², 2391534, F₃, 4, 15) (dual of [(2391534, 4), 9565934, 16]-NRT-code)	[i]