MinT - Information on Result #1612788

Information on Result #1612788

Linear OOA(3²⁴⁶, 58054, F₃, 4, 33) (dual of [(58054, 4), 231970, 34]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁴⁶, 58054, F₃, 3, 33) (dual of [(58054, 3), 173916, 34]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²⁴⁶, 59057, F₃, 3, 33) (dual of [(59057, 3), 176925, 34]-NRT-code), using
- 3² times duplication [i] based on linear OOA(3²⁴⁴, 59057, F₃, 3, 33) (dual of [(59057, 3), 176927, 34]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3²⁴⁴, 177171, F₃, 33) (dual of [177171, 176927, 34]-code), using
    - constructionÂ X applied to C([0,16]) âŠ‚ C([0,15]) [i] based on
      1. linear OA(3²⁴³, 177148, F₃, 33) (dual of [177148, 176905, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148Â | 3²²âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]
      2. linear OA(3²²¹, 177148, F₃, 31) (dual of [177148, 176927, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148Â | 3²²âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [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(3²⁴⁶, 14513, F₃, 36, 33) (dual of [(14513, 36), 522222, 34]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row