MinT - Information on Result #2487588

Information on Result #2487588

Linear OOA(3²²⁵, 29551, F₃, 2, 32) (dual of [(29551, 2), 58877, 33]-NRT-code), using 3¹ times duplication based on linear OOA(3²²⁴, 29551, F₃, 2, 32) (dual of [(29551, 2), 58878, 33]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(3²²², 29550, F₃, 2, 32) (dual of [(29550, 2), 58878, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3²²², 59100, F₃, 32) (dual of [59100, 58878, 33]-code), using
  - constructionÂ X applied to C_e(31) âŠ‚ C_e(25) [i] based on
    1. 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]
    2. 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]
    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: Constructive and 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		Method
1	Linear OOA(3²²⁵, 27198, F₃, 3, 32) (dual of [(27198, 3), 81369, 33]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²²⁵, 27198, F₃, 4, 32) (dual of [(27198, 4), 108567, 33]-NRT-code)	[i]
3	Linear OOA(3²²⁵, 27198, F₃, 5, 32) (dual of [(27198, 5), 135765, 33]-NRT-code)	[i]
4	Digital (193, 225, 27198)-net over F₃	[i]