MinT - Information on Result #2486137

Information on Result #2486137

Linear OOA(3¹⁰⁸, 29538, F₃, 2, 16) (dual of [(29538, 2), 58968, 17]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3¹⁰⁶, 29537, F₃, 2, 16) (dual of [(29537, 2), 58968, 17]-NRT-code), using

OOA 2-folding [i] based on linear OA(3¹⁰⁶, 59074, F₃, 16) (dual of [59074, 58968, 17]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3¹⁰⁵, 59073, F₃, 16) (dual of [59073, 58968, 17]-code), using
  - constructionÂ X applied to C_e(15) âŠ‚ C_e(12) [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(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(3⁴, 24, F₃, 2) (dual of [24, 20, 3]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
        Hamming code H(4,3) [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(3¹⁰⁸, 22005, F₃, 3, 16) (dual of [(22005, 3), 65907, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁰⁸, 22005, F₃, 4, 16) (dual of [(22005, 4), 87912, 17]-NRT-code)	[i]
3	Linear OOA(3¹⁰⁸, 22005, F₃, 5, 16) (dual of [(22005, 5), 109917, 17]-NRT-code)	[i]
4	Digital (92, 108, 22005)-net over F₃	[i]