MinT - Information on Result #1410614

Information on Result #1410614

Linear OOA(3¹³⁸, 2072, F₃, 2, 27) (dual of [(2072, 2), 4006, 28]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3¹³⁸, 2072, F₃, 27) (dual of [2072, 1934, 28]-code), using

discarding factors / shortening the dual code based on linear OA(3¹³⁸, 2227, F₃, 27) (dual of [2227, 2089, 28]-code), using
- constructionÂ X applied to C([0,13]) âŠ‚ C([0,10]) [i] based on
  1. linear OA(3¹²⁷, 2188, F₃, 27) (dual of [2188, 2061, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188Â | 3¹⁴âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
  2. linear OA(3⁹⁹, 2188, F₃, 21) (dual of [2188, 2089, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188Â | 3¹⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
  3. linear OA(3¹¹, 39, F₃, 5) (dual of [39, 28, 6]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹¹, 40, F₃, 5) (dual of [40, 29, 6]-code), using
      - (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
        linear OA(3¹, 13, F₃, 1) (dual of [13, 12, 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]
        linear OA(3³, 13, F₃, 2) (dual of [13, 10, 3]-code), using
        Hamming code H(3,3) [i]
        linear OA(3⁷, 14, F₃, 5) (dual of [14, 7, 6]-code), using
        extended quadratic residue code Q_e(14,3) [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(3¹³⁸, 1036, F₃, 3, 27) (dual of [(1036, 3), 2970, 28]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3¹³⁸, 1036, F₃, 4, 27) (dual of [(1036, 4), 4006, 28]-NRT-code)	[i]		OOA Folding