MinT - Information on Result #1414312

Information on Result #1414312

Linear OOA(3¹⁹³, 2157, F₃, 2, 39) (dual of [(2157, 2), 4121, 40]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3¹⁹³, 2157, F₃, 39) (dual of [2157, 1964, 40]-code), using

discarding factors / shortening the dual code based on linear OA(3¹⁹³, 2224, F₃, 39) (dual of [2224, 2031, 40]-code), using
- constructionÂ X applied to C([0,19]) âŠ‚ C([0,16]) [i] based on
  1. linear OA(3¹⁸³, 2188, F₃, 39) (dual of [2188, 2005, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188Â | 3¹⁴âˆ’1, defining interval IÂ =Â [0,19], and minimum distance dÂ â‰¥ |{−19,−18,…,19}|+1Â =Â 40 (BCH-bound) [i]
  2. linear OA(3¹⁵⁵, 2188, F₃, 33) (dual of [2188, 2033, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188Â | 3¹⁴âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]
  3. linear OA(3¹⁰, 36, F₃, 5) (dual of [36, 26, 6]-code), using
    - (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
      1. linear OA(3¹, 12, F₃, 1) (dual of [12, 11, 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]
      2. linear OA(3³, 12, F₃, 2) (dual of [12, 9, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(3³, 13, F₃, 2) (dual of [13, 10, 3]-code), using
        Hamming code H(3,3) [i]
      3. linear OA(3⁶, 12, F₃, 5) (dual of [12, 6, 6]-code), using
        extended Golay code G_e(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(3¹⁹³, 1078, F₃, 3, 39) (dual of [(1078, 3), 3041, 40]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3¹⁹³, 1078, F₃, 4, 39) (dual of [(1078, 4), 4119, 40]-NRT-code)	[i]		OOA Folding