MinT - Information on Result #953872

Information on Result #953872

Linear OOA(3²⁰⁴, 59058, F₃, 3, 28) (dual of [(59058, 3), 176970, 29]-NRT-code), using OOA 3-folding based on linear OA(3²⁰⁴, 177174, F₃, 28) (dual of [177174, 176970, 29]-code), using

1 times code embedding in larger space [i] based on linear OA(3²⁰³, 177173, F₃, 28) (dual of [177173, 176970, 29]-code), using
- constructionÂ X applied to C_e(27) âŠ‚ C_e(24) [i] based on
  1. linear OA(3¹⁹⁹, 177147, F₃, 28) (dual of [177147, 176948, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
  2. linear OA(3¹⁷⁷, 177147, F₃, 25) (dual of [177147, 176970, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
  3. linear OA(3⁴, 26, F₃, 2) (dual of [26, 22, 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(3²⁰⁴, 59058, F₃, 3, 27) (dual of [(59058, 3), 176970, 28]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(3²⁰⁵, 59058, F₃, 3, 28) (dual of [(59058, 3), 176969, 29]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(3²⁰⁶, 59058, F₃, 3, 28) (dual of [(59058, 3), 176968, 29]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(3²⁰⁴, 48531, F₃, 4, 28) (dual of [(48531, 4), 193920, 29]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
5	Linear OOA(3²⁰⁴, 48531, F₃, 5, 28) (dual of [(48531, 5), 242451, 29]-NRT-code)	[i]
6	Digital (176, 204, 48531)-net over F₃	[i]