MinT - Information on Result #1611343

Information on Result #1611343

Linear OOA(3²³¹, 26382, F₃, 4, 33) (dual of [(26382, 4), 105297, 34]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²³¹, 26382, F₃, 2, 33) (dual of [(26382, 2), 52533, 34]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²³¹, 29549, F₃, 2, 33) (dual of [(29549, 2), 58867, 34]-NRT-code), using
- 1 step truncation [i] based on linear OOA(3²³², 29550, F₃, 2, 34) (dual of [(29550, 2), 58868, 35]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3²³², 59100, F₃, 34) (dual of [59100, 58868, 35]-code), using
    - constructionÂ X applied to C_e(33) âŠ‚ C_e(27) [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(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(3¹¹, 51, F₃, 5) (dual of [51, 40, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹¹, 85, F₃, 5) (dual of [85, 74, 6]-code), using
        codes constructed by inverting constructionÂ Y₁ [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(3²³¹, 6595, F₃, 36, 33) (dual of [(6595, 36), 237189, 34]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row