MinT - Information on Result #1524265

Information on Result #1524265

Linear OOA(3¹⁴⁹, 1562, F₃, 3, 31) (dual of [(1562, 3), 4537, 32]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3¹⁴⁹, 1562, F₃, 31) (dual of [1562, 1413, 32]-code), using

discarding factors / shortening the dual code based on linear OA(3¹⁴⁹, 2216, F₃, 31) (dual of [2216, 2067, 32]-code), using
- constructionÂ X applied to C([0,15]) âŠ‚ C([0,12]) [i] based on
  1. linear OA(3¹⁴¹, 2188, F₃, 31) (dual of [2188, 2047, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188Â | 3¹⁴âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]
  2. linear OA(3¹¹³, 2188, F₃, 25) (dual of [2188, 2075, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188Â | 3¹⁴âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
  3. linear OA(3⁸, 28, F₃, 5) (dual of [28, 20, 6]-code), using
    - dual code (with bound on d by constructionÂ Y1) [i] based on
      1. linear OA(3²⁰, 28, F₃, 14) (dual of [28, 8, 15]-code), using
        contraction [i] based on linear OA(3⁴⁸, 56, F₃, 29) (dual of [56, 8, 30]-code), using the BCH-code C(I) with length 56Â | 3⁶âˆ’1, defining interval IÂ =Â {0,1,…,28}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
      2. nonexistence of linear OA(3¹⁹, 23, F₃, 14) (dual of [23, 4, 15]-code), because
        2 times truncation [i] would yield linear OA(3¹⁷, 21, F₃, 12) (dual of [21, 4, 13]-code), but
        â€œHNâ€ bound on codes from Brouwerâ€™s database [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(3¹⁴⁹, 781, F₃, 5, 31) (dual of [(781, 5), 3756, 32]-NRT-code)	[i]		OOA Folding