MinT - Information on Result #813169

Information on Result #813169

Linear OOA(3¹⁰¹, 29529, F₃, 2, 15) (dual of [(29529, 2), 58957, 16]-NRT-code), using OOA 2-folding based on linear OA(3¹⁰¹, 59058, F₃, 15) (dual of [59058, 58957, 16]-code), using

discarding factors / shortening the dual code based on linear OA(3¹⁰¹, 59059, F₃, 15) (dual of [59059, 58958, 16]-code), using
- 1 times truncation [i] based on linear OA(3¹⁰², 59060, F₃, 16) (dual of [59060, 58958, 17]-code), using
  - constructionÂ X applied to C_e(15) âŠ‚ C_e(13) [i] based on
    1. 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]
    2. linear OA(3⁹¹, 59049, F₃, 14) (dual of [59049, 58958, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
    3. linear OA(3¹, 11, F₃, 1) (dual of [11, 10, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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(3¹⁰¹, 22823, F₃, 3, 15) (dual of [(22823, 3), 68368, 16]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁰¹, 22823, F₃, 4, 15) (dual of [(22823, 4), 91191, 16]-NRT-code)	[i]
3	Linear OOA(3¹⁰¹, 22823, F₃, 5, 15) (dual of [(22823, 5), 114014, 16]-NRT-code)	[i]
4	Digital (86, 101, 22823)-net over F₃	[i]