MinT - Information on Result #817501

Information on Result #817501

Linear OOA(3²⁴³, 1113, F₃, 2, 50) (dual of [(1113, 2), 1983, 51]-NRT-code), using OOA 2-folding based on linear OA(3²⁴³, 2226, F₃, 50) (dual of [2226, 1983, 51]-code), using

constructionÂ X applied to C_e(49) âŠ‚ C_e(43) [i] based on
1. linear OA(3²³², 2187, F₃, 50) (dual of [2187, 1955, 51]-code), using an extension C_e(49) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,49], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 50 [i]
2. linear OA(3²⁰⁴, 2187, F₃, 44) (dual of [2187, 1983, 45]-code), using an extension C_e(43) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,43], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 44 [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
      1. 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]
      2. linear OA(3³, 13, F₃, 2) (dual of [13, 10, 3]-code), using
        Hamming code H(3,3) [i]
      3. linear OA(3⁷, 14, F₃, 5) (dual of [14, 7, 6]-code), using
        extended quadratic residue code Q_e(14,3) [i]

Mode: Constructive and 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(3²⁴⁵, 1114, F₃, 2, 50) (dual of [(1114, 2), 1983, 51]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
2	Linear OOA(3²⁴⁴, 1113, F₃, 2, 50) (dual of [(1113, 2), 1982, 51]-NRT-code)	[i]		OOA Duplication