MinT - Information on Result #1648968

Information on Result #1648968

Linear OOA(3²¹⁰, 45387, F₃, 5, 29) (dual of [(45387, 5), 226725, 30]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²¹⁰, 45387, F₃, 3, 29) (dual of [(45387, 3), 135951, 30]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²¹⁰, 59052, F₃, 3, 29) (dual of [(59052, 3), 176946, 30]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3²¹⁰, 177156, F₃, 29) (dual of [177156, 176946, 30]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²¹⁰, 177158, F₃, 29) (dual of [177158, 176948, 30]-code), using
    - constructionÂ X applied to C_e(28) âŠ‚ C_e(27) [i] based on
      1. linear OA(3²¹⁰, 177147, F₃, 29) (dual of [177147, 176937, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
      2. linear OA(3¹⁹⁹, 177147, F₃, 28) (dual of [177147, 176948, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
      3. linear OA(3⁰, 11, F₃, 0) (dual of [11, 11, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n 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(3²¹⁰, 15128, F₃, 35, 29) (dual of [(15128, 35), 529270, 30]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row