MinT - Information on Result #1418605

Information on Result #1418605

Linear OOA(3²³⁹, 4709, F₃, 2, 43) (dual of [(4709, 2), 9179, 44]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3²³⁹, 4709, F₃, 43) (dual of [4709, 4470, 44]-code), using

discarding factors / shortening the dual code based on linear OA(3²³⁹, 6608, F₃, 43) (dual of [6608, 6369, 44]-code), using
- 3 times code embedding in larger space [i] based on linear OA(3²³⁶, 6605, F₃, 43) (dual of [6605, 6369, 44]-code), using
  - constructionÂ X applied to C([0,21]) âŠ‚ C([0,18]) [i] based on
    1. linear OA(3²²⁵, 6562, F₃, 43) (dual of [6562, 6337, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 3¹⁶âˆ’1, defining interval IÂ =Â [0,21], and minimum distance dÂ â‰¥ |{−21,−20,…,21}|+1Â =Â 44 (BCH-bound) [i]
    2. linear OA(3¹⁹³, 6562, F₃, 37) (dual of [6562, 6369, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 3¹⁶âˆ’1, defining interval IÂ =Â [0,18], and minimum distance dÂ â‰¥ |{−18,−17,…,18}|+1Â =Â 38 (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(3²³⁹, 2354, F₃, 3, 43) (dual of [(2354, 3), 6823, 44]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3²³⁹, 2354, F₃, 4, 43) (dual of [(2354, 4), 9177, 44]-NRT-code)	[i]		OOA Folding