MinT - Information on Result #1059775

Information on Result #1059775

Linear OOA(3¹⁴², 2391488, F₃, 4, 12) (dual of [(2391488, 4), 9565810, 13]-NRT-code), using OOA 2-folding based on linear OOA(3¹⁴², 4782976, F₃, 2, 12) (dual of [(4782976, 2), 9565810, 13]-NRT-code), using

trace code [i] based on linear OOA(9⁷¹, 2391488, F₉, 2, 12) (dual of [(2391488, 2), 4782905, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(9⁷¹, 4782976, F₉, 12) (dual of [4782976, 4782905, 13]-code), using
  - constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
    1. linear OA(9⁷¹, 4782969, F₉, 12) (dual of [4782969, 4782898, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
    2. linear OA(9⁶⁴, 4782969, F₉, 11) (dual of [4782969, 4782905, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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(3¹⁴³, 2391488, F₃, 4, 12) (dual of [(2391488, 4), 9565809, 13]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3¹⁴⁹, 2391495, F₃, 4, 12) (dual of [(2391495, 4), 9565831, 13]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(3¹⁵¹, 2391501, F₃, 4, 12) (dual of [(2391501, 4), 9565853, 13]-NRT-code)	[i]
4	Linear OOA(3¹⁵², 2391507, F₃, 4, 12) (dual of [(2391507, 4), 9565876, 13]-NRT-code)	[i]
5	Linear OOA(3¹⁵³, 2391513, F₃, 4, 12) (dual of [(2391513, 4), 9565899, 13]-NRT-code)	[i]
6	Linear OOA(3¹⁵⁴, 2391521, F₃, 4, 12) (dual of [(2391521, 4), 9565930, 13]-NRT-code)	[i]
7	Linear OOA(3¹⁵⁵, 2391530, F₃, 4, 12) (dual of [(2391530, 4), 9565965, 13]-NRT-code)	[i]
8	Linear OOA(3¹⁵⁸, 2391534, F₃, 4, 12) (dual of [(2391534, 4), 9565978, 13]-NRT-code)	[i]
9	Linear OOA(3¹⁵⁹, 2391541, F₃, 4, 12) (dual of [(2391541, 4), 9566005, 13]-NRT-code)	[i]
10	Linear OOA(3¹⁶⁰, 2391572, F₃, 4, 12) (dual of [(2391572, 4), 9566128, 13]-NRT-code)	[i]