MinT - Information on Result #1520675

Information on Result #1520675

Linear OOA(3⁵⁸, 1055, F₃, 3, 13) (dual of [(1055, 3), 3107, 14]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3⁵⁸, 1055, F₃, 2, 13) (dual of [(1055, 2), 2052, 14]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3⁵⁸, 1097, F₃, 2, 13) (dual of [(1097, 2), 2136, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3⁵⁸, 2194, F₃, 13) (dual of [2194, 2136, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁵⁸, 2195, F₃, 13) (dual of [2195, 2137, 14]-code), using
    - constructionÂ X applied to C_e(12) âŠ‚ C_e(10) [i] based on
      1. linear OA(3⁵⁷, 2187, F₃, 13) (dual of [2187, 2130, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      2. linear OA(3⁵⁰, 2187, F₃, 11) (dual of [2187, 2137, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      3. linear OA(3¹, 8, F₃, 1) (dual of [8, 7, 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]

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(3⁵⁸, 527, F₃, 5, 13) (dual of [(527, 5), 2577, 14]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3⁵⁸, 527, F₃, 15, 13) (dual of [(527, 15), 7847, 14]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row