MinT - Information on Result #1418815

Information on Result #1418815

Linear OOA(3²⁴¹, 2232, F₃, 2, 50) (dual of [(2232, 2), 4223, 51]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3²⁴¹, 2232, F₃, 50) (dual of [2232, 1991, 51]-code), using

discarding factors / shortening the dual code based on linear OA(3²⁴¹, 2244, F₃, 50) (dual of [2244, 2003, 51]-code), using
- 41 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (3, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 6 times 0, 1, 9 times 0, 1, 13 times 0) [i] based on linear OA(3²³², 2194, F₃, 50) (dual of [2194, 1962, 51]-code), using
  - constructionÂ X applied to C_e(49) âŠ‚ C_e(48) [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(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(3⁰, 7, F₃, 0) (dual of [7, 7, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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(3²⁴¹, 1116, F₃, 3, 50) (dual of [(1116, 3), 3107, 51]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3²⁴¹, 1116, F₃, 4, 50) (dual of [(1116, 4), 4223, 51]-NRT-code)	[i]		OOA Folding