MinT - Information on Result #895074

Information on Result #895074

Linear OOA(3¹⁶⁹, 4783018, F₃, 2, 13) (dual of [(4783018, 2), 9565867, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹³, 42, F₃, 2, 6) (dual of [(42, 2), 71, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (7, 13, 42)-net over F₃, using
  - linear code embedding found in a computer search [i]
linear OOA(3¹⁵⁶, 4782976, F₃, 2, 13) (dual of [(4782976, 2), 9565796, 14]-NRT-code), using
- trace code [i] based on linear OOA(9⁷⁸, 2391488, F₉, 2, 13) (dual of [(2391488, 2), 4782898, 14]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(9⁷⁸, 4782976, F₉, 13) (dual of [4782976, 4782898, 14]-code), using
    - constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
      1. linear OA(9⁷⁸, 4782969, F₉, 13) (dual of [4782969, 4782891, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      2. 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]
      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.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹⁷⁰, 4783018, F₃, 2, 13) (dual of [(4783018, 2), 9565866, 14]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3¹⁶⁹, 2391509, F₃, 4, 13) (dual of [(2391509, 4), 9565867, 14]-NRT-code)	[i]		OOA Folding