MinT - Information on Result #813362

Information on Result #813362

Linear OOA(3¹¹⁶, 29537, F₃, 2, 17) (dual of [(29537, 2), 58958, 18]-NRT-code), using OOA 2-folding based on linear OA(3¹¹⁶, 59074, F₃, 17) (dual of [59074, 58958, 18]-code), using

1 times code embedding in larger space [i] based on linear OA(3¹¹⁵, 59073, F₃, 17) (dual of [59073, 58958, 18]-code), using
- constructionÂ X applied to C_e(16) âŠ‚ C_e(13) [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(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(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(3¹¹⁶, 23191, F₃, 3, 17) (dual of [(23191, 3), 69457, 18]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹¹⁶, 23191, F₃, 4, 17) (dual of [(23191, 4), 92648, 18]-NRT-code)	[i]
3	Linear OOA(3¹¹⁶, 23191, F₃, 5, 17) (dual of [(23191, 5), 115839, 18]-NRT-code)	[i]
4	Digital (99, 116, 23191)-net over F₃	[i]