MinT - Information on Result #1414558

Information on Result #1414558

Linear OOA(3¹⁹⁶, 6197, F₃, 2, 33) (dual of [(6197, 2), 12198, 34]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3¹⁹⁶, 6197, F₃, 33) (dual of [6197, 6001, 34]-code), using

discarding factors / shortening the dual code based on linear OA(3¹⁹⁶, 6629, F₃, 33) (dual of [6629, 6433, 34]-code), using
- 3 times code embedding in larger space [i] based on linear OA(3¹⁹³, 6626, F₃, 33) (dual of [6626, 6433, 34]-code), using
  - constructionÂ X applied to C([0,16]) âŠ‚ C([0,12]) [i] based on
    1. linear OA(3¹⁷⁷, 6562, F₃, 33) (dual of [6562, 6385, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 3¹⁶âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (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(3¹⁶, 64, F₃, 7) (dual of [64, 48, 8]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹⁶, 82, F₃, 7) (dual of [82, 66, 8]-code), using
        generator matrices provided on Edelâ€™s homepage [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(3¹⁹⁶, 3098, F₃, 3, 33) (dual of [(3098, 3), 9098, 34]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3¹⁹⁶, 3098, F₃, 4, 33) (dual of [(3098, 4), 12196, 34]-NRT-code)	[i]		OOA Folding