MinT - Information on Result #1650112

Information on Result #1650112

Linear OOA(3²²³, 18966, F₃, 5, 34) (dual of [(18966, 5), 94607, 35]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²²³, 18966, F₃, 3, 34) (dual of [(18966, 3), 56675, 35]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²²³, 19687, F₃, 3, 34) (dual of [(19687, 3), 58838, 35]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3²²³, 59061, F₃, 34) (dual of [59061, 58838, 35]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(3²²², 59060, F₃, 34) (dual of [59060, 58838, 35]-code), using
    - constructionÂ X applied to C_e(33) âŠ‚ C_e(31) [i] based on
      1. linear OA(3²²¹, 59049, F₃, 34) (dual of [59049, 58828, 35]-code), using an extension C_e(33) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,33], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [i]
      2. linear OA(3²¹¹, 59049, F₃, 32) (dual of [59049, 58838, 33]-code), using an extension C_e(31) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,31], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 32 [i]
      3. linear OA(3¹, 11, F₃, 1) (dual of [11, 10, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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(3²²³, 4741, F₃, 45, 34) (dual of [(4741, 45), 213122, 35]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row