MinT - Information on Result #1408948

Information on Result #1408948

Linear OOA(3¹⁰³, 1892, F₃, 2, 20) (dual of [(1892, 2), 3681, 21]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3¹⁰³, 1892, F₃, 20) (dual of [1892, 1789, 21]-code), using

discarding factors / shortening the dual code based on linear OA(3¹⁰³, 2226, F₃, 20) (dual of [2226, 2123, 21]-code), using
- constructionÂ X applied to C_e(19) âŠ‚ C_e(13) [i] based on
  1. linear OA(3⁹², 2187, F₃, 20) (dual of [2187, 2095, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
  2. linear OA(3⁶⁴, 2187, F₃, 14) (dual of [2187, 2123, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [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(3¹⁰³, 946, F₃, 3, 20) (dual of [(946, 3), 2735, 21]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3¹⁰³, 946, F₃, 4, 20) (dual of [(946, 4), 3681, 21]-NRT-code)	[i]		OOA Folding