MinT - Information on Result #1650115

Information on Result #1650115

Linear OOA(3²²³, 57445, F₃, 5, 30) (dual of [(57445, 5), 287002, 31]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²²³, 57445, F₃, 3, 30) (dual of [(57445, 3), 172112, 31]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²²³, 59057, F₃, 3, 30) (dual of [(59057, 3), 176948, 31]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3²²³, 177171, F₃, 30) (dual of [177171, 176948, 31]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(3²²², 177170, F₃, 30) (dual of [177170, 176948, 31]-code), using
    - constructionÂ X applied to C_e(30) âŠ‚ C_e(27) [i] based on
      1. 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]
      2. linear OA(3¹⁹⁹, 177147, F₃, 28) (dual of [177147, 176948, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
      3. linear OA(3¹, 23, F₃, 1) (dual of [23, 22, 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(3²²³, 19148, F₃, 35, 30) (dual of [(19148, 35), 669957, 31]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row