MinT - Information on Result #812781

Information on Result #812781

Linear OOA(3⁶⁶, 29537, F₃, 2, 10) (dual of [(29537, 2), 59008, 11]-NRT-code), using OOA 2-folding based on linear OA(3⁶⁶, 59074, F₃, 10) (dual of [59074, 59008, 11]-code), using

1 times code embedding in larger space [i] based on linear OA(3⁶⁵, 59073, F₃, 10) (dual of [59073, 59008, 11]-code), using
- constructionÂ X applied to C_e(9) âŠ‚ C_e(6) [i] based on
  1. linear OA(3⁶¹, 59049, F₃, 10) (dual of [59049, 58988, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
  2. linear OA(3⁴¹, 59049, F₃, 7) (dual of [59049, 59008, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [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(3⁶⁶, 29537, F₃, 3, 10) (dual of [(29537, 3), 88545, 11]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3⁶⁶, 29537, F₃, 4, 10) (dual of [(29537, 4), 118082, 11]-NRT-code)	[i]
3	Linear OOA(3⁶⁶, 29537, F₃, 5, 10) (dual of [(29537, 5), 147619, 11]-NRT-code)	[i]
4	Digital (56, 66, 29537)-net over F₃	[i]