MinT - Information on Result #1419139

Information on Result #1419139

Linear OOA(3²⁴⁴, 1984, F₃, 2, 52) (dual of [(1984, 2), 3724, 53]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3²⁴⁴, 1984, F₃, 52) (dual of [1984, 1740, 53]-code), using

discarding factors / shortening the dual code based on linear OA(3²⁴⁴, 2206, F₃, 52) (dual of [2206, 1962, 53]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3²⁴³, 2205, F₃, 52) (dual of [2205, 1962, 53]-code), using
  - constructionÂ X applied to C_e(51) âŠ‚ C_e(48) [i] based on
    1. linear OA(3²³⁹, 2187, F₃, 52) (dual of [2187, 1948, 53]-code), using an extension C_e(51) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,51], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 52 [i]
    2. linear OA(3²²⁵, 2187, F₃, 49) (dual of [2187, 1962, 50]-code), using an extension C_e(48) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,48], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 49 [i]
    3. linear OA(3⁴, 18, F₃, 2) (dual of [18, 14, 3]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
        Hamming code H(4,3) [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(3²⁴⁴, 992, F₃, 3, 52) (dual of [(992, 3), 2732, 53]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3²⁴⁴, 992, F₃, 4, 52) (dual of [(992, 4), 3724, 53]-NRT-code)	[i]		OOA Folding