MinT - Information on Result #1414002

Information on Result #1414002

Linear OOA(3¹⁸⁹, 1688, F₃, 2, 40) (dual of [(1688, 2), 3187, 41]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3¹⁸⁹, 1688, F₃, 40) (dual of [1688, 1499, 41]-code), using

discarding factors / shortening the dual code based on linear OA(3¹⁸⁹, 2208, F₃, 40) (dual of [2208, 2019, 41]-code), using
- constructionÂ XX applied to C_e(39) âŠ‚ C_e(36) âŠ‚ C_e(34) [i] based on
  1. linear OA(3¹⁸³, 2187, F₃, 40) (dual of [2187, 2004, 41]-code), using an extension C_e(39) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,39], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 40 [i]
  2. linear OA(3¹⁶⁹, 2187, F₃, 37) (dual of [2187, 2018, 38]-code), using an extension C_e(36) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,36], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [i]
  3. linear OA(3¹⁶², 2187, F₃, 35) (dual of [2187, 2025, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
  4. linear OA(3⁴, 19, F₃, 2) (dual of [19, 15, 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]
  5. linear OA(3¹, 2, F₃, 1) (dual of [2, 1, 2]-code), using
    - dual of repetition code with length 2 [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(3¹⁸⁹, 844, F₃, 3, 40) (dual of [(844, 3), 2343, 41]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3¹⁸⁹, 844, F₃, 4, 40) (dual of [(844, 4), 3187, 41]-NRT-code)	[i]		OOA Folding