MinT - Information on Result #2678167

Information on Result #2678167

Linear OOA(3²¹², 59053, F₃, 3, 29) (dual of [(59053, 3), 176947, 30]-NRT-code), using 3¹ times duplication based on linear OOA(3²¹¹, 59053, F₃, 3, 29) (dual of [(59053, 3), 176948, 30]-NRT-code), using

OOA 3-folding [i] based on linear OA(3²¹¹, 177159, F₃, 29) (dual of [177159, 176948, 30]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3²¹⁰, 177158, F₃, 29) (dual of [177158, 176948, 30]-code), using
  - constructionÂ X applied to C_e(28) âŠ‚ C_e(27) [i] based on
    1. linear OA(3²¹⁰, 177147, F₃, 29) (dual of [177147, 176937, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
    2. 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]
    3. linear OA(3⁰, 11, F₃, 0) (dual of [11, 11, 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(3²¹², 49559, F₃, 4, 29) (dual of [(49559, 4), 198024, 30]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²¹², 49559, F₃, 5, 29) (dual of [(49559, 5), 247583, 30]-NRT-code)	[i]
3	Digital (183, 212, 49559)-net over F₃	[i]