MinT - Information on Result #1416095

Information on Result #1416095

Linear OOA(3²¹⁴, 1909, F₃, 2, 45) (dual of [(1909, 2), 3604, 46]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3²¹⁴, 1909, F₃, 45) (dual of [1909, 1695, 46]-code), using

discarding factors / shortening the dual code based on linear OA(3²¹⁴, 2205, F₃, 45) (dual of [2205, 1991, 46]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3²¹², 2203, F₃, 45) (dual of [2203, 1991, 46]-code), using
  - constructionÂ X applied to C([0,22]) âŠ‚ C([0,21]) [i] based on
    1. linear OA(3²¹¹, 2188, F₃, 45) (dual of [2188, 1977, 46]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188Â | 3¹⁴âˆ’1, defining interval IÂ =Â [0,22], and minimum distance dÂ â‰¥ |{−22,−21,…,22}|+1Â =Â 46 (BCH-bound) [i]
    2. linear OA(3¹⁹⁷, 2188, F₃, 43) (dual of [2188, 1991, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188Â | 3¹⁴âˆ’1, defining interval IÂ =Â [0,21], and minimum distance dÂ â‰¥ |{−21,−20,…,21}|+1Â =Â 44 (BCH-bound) [i]
    3. linear OA(3¹, 15, F₃, 1) (dual of [15, 14, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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(3²¹⁴, 954, F₃, 3, 45) (dual of [(954, 3), 2648, 46]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3²¹⁴, 954, F₃, 4, 45) (dual of [(954, 4), 3602, 46]-NRT-code)	[i]		OOA Folding