MinT - Information on Result #1642331

Information on Result #1642331

Linear OOA(3¹⁰³, 1987533, F₃, 5, 11) (dual of [(1987533, 5), 9937562, 12]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁰³, 1987533, F₃, 2, 11) (dual of [(1987533, 2), 3974963, 12]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁰³, 2391500, F₃, 2, 11) (dual of [(2391500, 2), 4782897, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁰³, 4783000, F₃, 11) (dual of [4783000, 4782897, 12]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁰³, 4783001, F₃, 11) (dual of [4783001, 4782898, 12]-code), using
    - constructionÂ X applied to C_e(10) âŠ‚ C_e(7) [i] based on
      1. linear OA(3⁹⁹, 4782969, F₃, 11) (dual of [4782969, 4782870, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      2. linear OA(3⁷¹, 4782969, F₃, 8) (dual of [4782969, 4782898, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      3. linear OA(3⁴, 32, F₃, 2) (dual of [32, 28, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
        Hamming code H(4,3) [i]

Mode: 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(3¹⁰³, 1987532, F₃, 15, 11) (dual of [(1987532, 15), 29812877, 12]-NRT-code)	[i]		OOA Stacking with Additional Row