MinT - Information on Result #1641722

Information on Result #1641722

Linear OOA(3⁸⁶, 1073, F₃, 5, 19) (dual of [(1073, 5), 5279, 20]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3⁸⁶, 1073, F₃, 2, 19) (dual of [(1073, 2), 2060, 20]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3⁸⁶, 1097, F₃, 2, 19) (dual of [(1097, 2), 2108, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3⁸⁶, 2194, F₃, 19) (dual of [2194, 2108, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁸⁶, 2195, F₃, 19) (dual of [2195, 2109, 20]-code), using
    - constructionÂ X applied to C_e(18) âŠ‚ C_e(16) [i] based on
      1. linear OA(3⁸⁵, 2187, F₃, 19) (dual of [2187, 2102, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      2. linear OA(3⁷⁸, 2187, F₃, 17) (dual of [2187, 2109, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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(3⁸⁶, 536, F₃, 25, 19) (dual of [(536, 25), 13314, 20]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row