MinT - Information on Result #1649664

Information on Result #1649664

Linear OOA(3²¹⁸, 7238, F₃, 5, 37) (dual of [(7238, 5), 35972, 38]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²¹⁸, 7238, F₃, 2, 37) (dual of [(7238, 2), 14258, 38]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²¹⁸, 9846, F₃, 2, 37) (dual of [(9846, 2), 19474, 38]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3²¹⁸, 19692, F₃, 37) (dual of [19692, 19474, 38]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²¹⁸, 19693, F₃, 37) (dual of [19693, 19475, 38]-code), using
    - constructionÂ X applied to C_e(36) âŠ‚ C_e(34) [i] based on
      1. linear OA(3²¹⁷, 19683, F₃, 37) (dual of [19683, 19466, 38]-code), using an extension C_e(36) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,36], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [i]
      2. linear OA(3²⁰⁸, 19683, F₃, 35) (dual of [19683, 19475, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
      3. linear OA(3¹, 10, F₃, 1) (dual of [10, 9, 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(3²¹⁸, 1809, F₃, 45, 37) (dual of [(1809, 45), 81187, 38]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row