MinT - Information on Result #1413852

Information on Result #1413852

Linear OOA(3¹⁸⁷, 2050, F₃, 2, 38) (dual of [(2050, 2), 3913, 39]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3¹⁸⁷, 2050, F₃, 38) (dual of [2050, 1863, 39]-code), using

discarding factors / shortening the dual code based on linear OA(3¹⁸⁷, 2226, F₃, 38) (dual of [2226, 2039, 39]-code), using
- constructionÂ X applied to C_e(37) âŠ‚ C_e(31) [i] based on
  1. linear OA(3¹⁷⁶, 2187, F₃, 38) (dual of [2187, 2011, 39]-code), using an extension C_e(37) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,37], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 38 [i]
  2. linear OA(3¹⁴⁸, 2187, F₃, 32) (dual of [2187, 2039, 33]-code), using an extension C_e(31) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,31], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 32 [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(3¹⁸⁷, 1025, F₃, 3, 38) (dual of [(1025, 3), 2888, 39]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3¹⁸⁷, 1025, F₃, 4, 38) (dual of [(1025, 4), 3913, 39]-NRT-code)	[i]		OOA Folding