MinT - Information on Result #1611534

Information on Result #1611534

Linear OOA(3²³³, 46874, F₃, 4, 32) (dual of [(46874, 4), 187263, 33]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²³³, 46874, F₃, 3, 32) (dual of [(46874, 3), 140389, 33]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²³³, 59053, F₃, 3, 32) (dual of [(59053, 3), 176926, 33]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3²³³, 177159, F₃, 32) (dual of [177159, 176926, 33]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(3²³², 177158, F₃, 32) (dual of [177158, 176926, 33]-code), using
    - constructionÂ X applied to C_e(31) âŠ‚ C_e(30) [i] based on
      1. linear OA(3²³², 177147, F₃, 32) (dual of [177147, 176915, 33]-code), using an extension C_e(31) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,31], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 32 [i]
      2. linear OA(3²²¹, 177147, F₃, 31) (dual of [177147, 176926, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
      3. linear OA(3⁰, 11, F₃, 0) (dual of [11, 11, 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(3²³³, 11718, F₃, 36, 32) (dual of [(11718, 36), 421615, 33]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row