MinT - Information on Result #1651882

Information on Result #1651882

Linear OOA(3²⁴², 18754, F₃, 5, 37) (dual of [(18754, 5), 93528, 38]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁴², 18754, F₃, 3, 37) (dual of [(18754, 3), 56020, 38]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²⁴², 19686, F₃, 3, 37) (dual of [(19686, 3), 58816, 38]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3²⁴², 59058, F₃, 37) (dual of [59058, 58816, 38]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²⁴², 59060, F₃, 37) (dual of [59060, 58818, 38]-code), using
    - constructionÂ X applied to C_e(36) âŠ‚ C_e(34) [i] based on
      1. linear OA(3²⁴¹, 59049, F₃, 37) (dual of [59049, 58808, 38]-code), using an extension C_e(36) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,36], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [i]
      2. linear OA(3²³¹, 59049, F₃, 35) (dual of [59049, 58818, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
      3. linear OA(3¹, 11, F₃, 1) (dual of [11, 10, 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(3²⁴², 4688, F₃, 45, 37) (dual of [(4688, 45), 210718, 38]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row