MinT - Information on Result #1412714

Information on Result #1412714

Linear OOA(3¹⁷¹, 4428, F₃, 2, 30) (dual of [(4428, 2), 8685, 31]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3¹⁷¹, 4428, F₃, 30) (dual of [4428, 4257, 31]-code), using

discarding factors / shortening the dual code based on linear OA(3¹⁷¹, 6604, F₃, 30) (dual of [6604, 6433, 31]-code), using
- 1 times truncation [i] based on linear OA(3¹⁷², 6605, F₃, 31) (dual of [6605, 6433, 32]-code), using
  - constructionÂ X applied to C([0,15]) âŠ‚ C([0,12]) [i] based on
    1. linear OA(3¹⁶¹, 6562, F₃, 31) (dual of [6562, 6401, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 3¹⁶âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]
    2. 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]
    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(3¹⁷¹, 2214, F₃, 3, 30) (dual of [(2214, 3), 6471, 31]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3¹⁷¹, 2214, F₃, 4, 30) (dual of [(2214, 4), 8685, 31]-NRT-code)	[i]		OOA Folding