MinT - Information on Result #1410674

Information on Result #1410674

Linear OOA(3¹³⁹, 4432, F₃, 2, 24) (dual of [(4432, 2), 8725, 25]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3¹³⁹, 4432, F₃, 24) (dual of [4432, 4293, 25]-code), using

discarding factors / shortening the dual code based on linear OA(3¹³⁹, 6604, F₃, 24) (dual of [6604, 6465, 25]-code), using
- 1 times truncation [i] based on linear OA(3¹⁴⁰, 6605, F₃, 25) (dual of [6605, 6465, 26]-code), using
  - constructionÂ X applied to C([0,12]) âŠ‚ C([0,9]) [i] based on
    1. linear OA(3¹²⁹, 6562, F₃, 25) (dual of [6562, 6433, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 3¹⁶âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
    2. linear OA(3⁹⁷, 6562, F₃, 19) (dual of [6562, 6465, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 3¹⁶âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
    3. linear OA(3¹¹, 43, F₃, 5) (dual of [43, 32, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹¹, 85, F₃, 5) (dual of [85, 74, 6]-code), using
        codes constructed by inverting constructionÂ Y₁ [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(3¹³⁹, 2216, F₃, 3, 24) (dual of [(2216, 3), 6509, 25]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3¹³⁹, 2216, F₃, 4, 24) (dual of [(2216, 4), 8725, 25]-NRT-code)	[i]		OOA Folding