MinT - Information on Result #1643162

Information on Result #1643162

Linear OOA(3¹²², 19570, F₃, 5, 19) (dual of [(19570, 5), 97728, 20]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹²², 19570, F₃, 3, 19) (dual of [(19570, 3), 58588, 20]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹²², 19686, F₃, 3, 19) (dual of [(19686, 3), 58936, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3¹²², 59058, F₃, 19) (dual of [59058, 58936, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹²², 59060, F₃, 19) (dual of [59060, 58938, 20]-code), using
    - constructionÂ X applied to C_e(18) âŠ‚ C_e(16) [i] based on
      1. linear OA(3¹²¹, 59049, F₃, 19) (dual of [59049, 58928, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      2. linear OA(3¹¹¹, 59049, F₃, 17) (dual of [59049, 58938, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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(3¹²², 9784, F₃, 25, 19) (dual of [(9784, 25), 244478, 20]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row