MinT - Information on Result #2678360

Information on Result #2678360

Linear OOA(3²²⁷, 59058, F₃, 3, 31) (dual of [(59058, 3), 176947, 32]-NRT-code), using 3¹ times duplication based on linear OOA(3²²⁶, 59058, F₃, 3, 31) (dual of [(59058, 3), 176948, 32]-NRT-code), using

OOA 3-folding [i] based on linear OA(3²²⁶, 177174, F₃, 31) (dual of [177174, 176948, 32]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3²²⁵, 177173, F₃, 31) (dual of [177173, 176948, 32]-code), using
  - constructionÂ X applied to C_e(30) âŠ‚ C_e(27) [i] based on
    1. linear OA(3²²¹, 177147, F₃, 31) (dual of [177147, 176926, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [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(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(3²²⁷, 49601, F₃, 4, 31) (dual of [(49601, 4), 198177, 32]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²²⁷, 49601, F₃, 5, 31) (dual of [(49601, 5), 247778, 32]-NRT-code)	[i]
3	Digital (196, 227, 49601)-net over F₃	[i]