MinT - Information on Result #1416379

Information on Result #1416379

Linear OOA(3²¹⁷, 1857, F₃, 2, 46) (dual of [(1857, 2), 3497, 47]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3²¹⁷, 1857, F₃, 46) (dual of [1857, 1640, 47]-code), using

discarding factors / shortening the dual code based on linear OA(3²¹⁷, 2208, F₃, 46) (dual of [2208, 1991, 47]-code), using
- constructionÂ XX applied to C_e(45) âŠ‚ C_e(42) âŠ‚ C_e(40) [i] based on
  1. linear OA(3²¹¹, 2187, F₃, 46) (dual of [2187, 1976, 47]-code), using an extension C_e(45) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,45], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 46 [i]
  2. linear OA(3¹⁹⁷, 2187, F₃, 43) (dual of [2187, 1990, 44]-code), using an extension C_e(42) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,42], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 43 [i]
  3. linear OA(3¹⁹⁰, 2187, F₃, 41) (dual of [2187, 1997, 42]-code), using an extension C_e(40) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,40], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 41 [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(3²¹⁷, 928, F₃, 3, 46) (dual of [(928, 3), 2567, 47]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3²¹⁷, 928, F₃, 4, 46) (dual of [(928, 4), 3495, 47]-NRT-code)	[i]		OOA Folding