MinT - Information on Result #2486235

Information on Result #2486235

Linear OOA(3¹¹⁴, 29531, F₃, 2, 17) (dual of [(29531, 2), 58948, 18]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3¹¹², 29530, F₃, 2, 17) (dual of [(29530, 2), 58948, 18]-NRT-code), using

OOA 2-folding [i] based on linear OA(3¹¹², 59060, F₃, 17) (dual of [59060, 58948, 18]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3¹¹¹, 59059, F₃, 17) (dual of [59059, 58948, 18]-code), using
  - constructionÂ X applied to C_e(16) âŠ‚ C_e(15) [i] based on
    1. linear OA(3¹¹¹, 59049, F₃, 17) (dual of [59049, 58938, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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(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(3¹¹⁴, 19820, F₃, 3, 17) (dual of [(19820, 3), 59346, 18]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹¹⁴, 19820, F₃, 4, 17) (dual of [(19820, 4), 79166, 18]-NRT-code)	[i]
3	Linear OOA(3¹¹⁴, 19820, F₃, 5, 17) (dual of [(19820, 5), 98986, 18]-NRT-code)	[i]
4	Digital (97, 114, 19820)-net over F₃	[i]