MinT - Information on Result #2487485

Information on Result #2487485

Linear OOA(3²¹⁹, 29558, F₃, 2, 31) (dual of [(29558, 2), 58897, 32]-NRT-code), using 3¹ times duplication based on linear OOA(3²¹⁸, 29558, F₃, 2, 31) (dual of [(29558, 2), 58898, 32]-NRT-code), using

OOA 2-folding [i] based on linear OA(3²¹⁸, 59116, F₃, 31) (dual of [59116, 58898, 32]-code), using
- constructionÂ X applied to C_e(30) âŠ‚ C_e(22) [i] based on
  1. linear OA(3²⁰¹, 59049, F₃, 31) (dual of [59049, 58848, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
  2. linear OA(3¹⁵¹, 59049, F₃, 23) (dual of [59049, 58898, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
  3. linear OA(3¹⁷, 67, F₃, 7) (dual of [67, 50, 8]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹⁷, 80, F₃, 7) (dual of [80, 63, 8]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [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(3²¹⁹, 28135, F₃, 3, 31) (dual of [(28135, 3), 84186, 32]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²¹⁹, 28135, F₃, 4, 31) (dual of [(28135, 4), 112321, 32]-NRT-code)	[i]
3	Linear OOA(3²¹⁹, 28135, F₃, 5, 31) (dual of [(28135, 5), 140456, 32]-NRT-code)	[i]
4	Digital (188, 219, 28135)-net over F₃	[i]