MinT - Information on Result #1609628

Information on Result #1609628

Linear OOA(3²¹², 59068, F₃, 4, 28) (dual of [(59068, 4), 236060, 29]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²¹², 59068, F₃, 3, 28) (dual of [(59068, 3), 176992, 29]-NRT-code), using

OOA 3-folding [i] based on linear OA(3²¹², 177204, F₃, 28) (dual of [177204, 176992, 29]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3²¹⁰, 177202, F₃, 28) (dual of [177202, 176992, 29]-code), using
  - constructionÂ X applied to C_e(27) âŠ‚ C_e(21) [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(3¹⁵⁵, 177147, F₃, 22) (dual of [177147, 176992, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
    3. linear OA(3¹¹, 55, F₃, 5) (dual of [55, 44, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹¹, 85, F₃, 5) (dual of [85, 74, 6]-code), using
        codes constructed by inverting constructionÂ Y₁ [i]

Mode: 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		This result only	Method
1	Linear OOA(3²¹³, 59068, F₃, 4, 28) (dual of [(59068, 4), 236059, 29]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3²¹⁴, 59068, F₃, 4, 28) (dual of [(59068, 4), 236058, 29]-NRT-code)	[i]		OOA Duplication