MinT - Information on Result #1646818

Information on Result #1646818

Linear OOA(3¹⁸³, 26780, F₃, 5, 26) (dual of [(26780, 5), 133717, 27]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁸³, 26780, F₃, 2, 26) (dual of [(26780, 2), 53377, 27]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁸³, 29550, F₃, 2, 26) (dual of [(29550, 2), 58917, 27]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3¹⁸², 29550, F₃, 2, 26) (dual of [(29550, 2), 58918, 27]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁸², 59100, F₃, 26) (dual of [59100, 58918, 27]-code), using
    - constructionÂ X applied to C_e(25) âŠ‚ C_e(19) [i] based on
      1. linear OA(3¹⁷¹, 59049, F₃, 26) (dual of [59049, 58878, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
      2. linear OA(3¹³¹, 59049, F₃, 20) (dual of [59049, 58918, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [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(3¹⁸³, 8926, F₃, 35, 26) (dual of [(8926, 35), 312227, 27]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row