MinT - Information on Result #1649935

Information on Result #1649935

Linear OOA(3²²¹, 52788, F₃, 5, 30) (dual of [(52788, 5), 263719, 31]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²²¹, 52788, F₃, 3, 30) (dual of [(52788, 3), 158143, 31]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²²¹, 59052, F₃, 3, 30) (dual of [(59052, 3), 176935, 31]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3²²¹, 177156, F₃, 30) (dual of [177156, 176935, 31]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²²¹, 177158, F₃, 30) (dual of [177158, 176937, 31]-code), using
    - 1 times truncation [i] based on linear OA(3²²², 177159, F₃, 31) (dual of [177159, 176937, 32]-code), using
      - constructionÂ X applied to C_e(30) âŠ‚ C_e(28) [i] based on
        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]
        linear OA(3²¹⁰, 177147, F₃, 29) (dual of [177147, 176937, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
        linear OA(3¹, 12, F₃, 1) (dual of [12, 11, 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(3²²¹, 17595, F₃, 35, 30) (dual of [(17595, 35), 615604, 31]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row