MinT - Information on Result #2678060

Information on Result #2678060

Linear OOA(3²⁰⁶, 59058, F₃, 3, 28) (dual of [(59058, 3), 176968, 29]-NRT-code), using 3² times duplication based on linear OOA(3²⁰⁴, 59058, F₃, 3, 28) (dual of [(59058, 3), 176970, 29]-NRT-code), using

OOA 3-folding [i] 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(3²⁰⁶, 53186, F₃, 4, 28) (dual of [(53186, 4), 212538, 29]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²⁰⁶, 53186, F₃, 5, 28) (dual of [(53186, 5), 265724, 29]-NRT-code)	[i]
3	Digital (178, 206, 53186)-net over F₃	[i]