MinT - Information on Result #1605283

Information on Result #1605283

Linear OOA(3¹⁵³, 24532, F₃, 4, 22) (dual of [(24532, 4), 97975, 23]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁵³, 24532, F₃, 2, 22) (dual of [(24532, 2), 48911, 23]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁵³, 29550, F₃, 2, 22) (dual of [(29550, 2), 58947, 23]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3¹⁵², 29550, F₃, 2, 22) (dual of [(29550, 2), 58948, 23]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁵², 59100, F₃, 22) (dual of [59100, 58948, 23]-code), using
    - constructionÂ X applied to C_e(21) âŠ‚ C_e(15) [i] based on
      1. linear OA(3¹⁴¹, 59049, F₃, 22) (dual of [59049, 58908, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      2. linear OA(3¹⁰¹, 59049, F₃, 16) (dual of [59049, 58948, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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(3¹⁵³, 8177, F₃, 28, 22) (dual of [(8177, 28), 228803, 23]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row