MinT - Information on Result #1610971

Information on Result #1610971

Linear OOA(3²²⁷, 22783, F₃, 4, 33) (dual of [(22783, 4), 90905, 34]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²²⁷, 22783, F₃, 2, 33) (dual of [(22783, 2), 45339, 34]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²²⁷, 29542, F₃, 2, 33) (dual of [(29542, 2), 58857, 34]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3²²⁷, 59084, F₃, 33) (dual of [59084, 58857, 34]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²²⁷, 59085, F₃, 33) (dual of [59085, 58858, 34]-code), using
    - constructionÂ X applied to C_e(33) âŠ‚ C_e(28) [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(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]
      3. linear OA(3⁶, 36, F₃, 3) (dual of [36, 30, 4]-code or 36-cap in PG(5,3)), using
        discarding factors / shortening the dual code based on linear OA(3⁶, 48, F₃, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
        large caps in PG(5,Â b) [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(3²²⁷, 5695, F₃, 36, 33) (dual of [(5695, 36), 204793, 34]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row