MinT - Information on Result #1647415

Information on Result #1647415

Linear OOA(3¹⁹¹, 19680, F₃, 5, 29) (dual of [(19680, 5), 98209, 30]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁹¹, 19680, F₃, 3, 29) (dual of [(19680, 3), 58849, 30]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁹¹, 19686, F₃, 3, 29) (dual of [(19686, 3), 58867, 30]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3¹⁹¹, 59058, F₃, 29) (dual of [59058, 58867, 30]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁹¹, 59059, F₃, 29) (dual of [59059, 58868, 30]-code), using
    - constructionÂ X applied to C_e(28) âŠ‚ C_e(27) [i] based on
      1. linear OA(3¹⁹¹, 59049, F₃, 29) (dual of [59049, 58858, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
      2. linear OA(3¹⁸¹, 59049, F₃, 28) (dual of [59049, 58868, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
      3. linear OA(3⁰, 10, F₃, 0) (dual of [10, 10, 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(3¹⁹¹, 6559, F₃, 35, 29) (dual of [(6559, 35), 229374, 30]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row