MinT - Information on Result #2485923

Information on Result #2485923

Linear OOA(3⁹⁴, 29531, F₃, 2, 14) (dual of [(29531, 2), 58968, 15]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3⁹², 29530, F₃, 2, 14) (dual of [(29530, 2), 58968, 15]-NRT-code), using

OOA 2-folding [i] based on linear OA(3⁹², 59060, F₃, 14) (dual of [59060, 58968, 15]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3⁹¹, 59059, F₃, 14) (dual of [59059, 58968, 15]-code), using
  - constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
    1. 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]
    2. linear OA(3⁸¹, 59049, F₃, 13) (dual of [59049, 58968, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    3. linear OA(3⁰, 10, F₃, 0) (dual of [10, 10, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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(3⁹⁴, 24003, F₃, 3, 14) (dual of [(24003, 3), 71915, 15]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3⁹⁴, 24003, F₃, 4, 14) (dual of [(24003, 4), 95918, 15]-NRT-code)	[i]
3	Linear OOA(3⁹⁴, 24003, F₃, 5, 14) (dual of [(24003, 5), 119921, 15]-NRT-code)	[i]
4	Digital (80, 94, 24003)-net over F₃	[i]