MinT - Information on Result #1410000

Information on Result #1410000

Linear OOA(3¹²⁶, 1826, F₃, 2, 25) (dual of [(1826, 2), 3526, 26]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3¹²⁶, 1826, F₃, 25) (dual of [1826, 1700, 26]-code), using

discarding factors / shortening the dual code based on linear OA(3¹²⁶, 2229, F₃, 25) (dual of [2229, 2103, 26]-code), using
- 3 times code embedding in larger space [i] based on linear OA(3¹²³, 2226, F₃, 25) (dual of [2226, 2103, 26]-code), using
  - constructionÂ X applied to C([0,12]) âŠ‚ C([0,9]) [i] based on
    1. 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]
    2. linear OA(3⁸⁵, 2188, F₃, 19) (dual of [2188, 2103, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188Â | 3¹⁴âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
    3. linear OA(3¹⁰, 38, F₃, 5) (dual of [38, 28, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹⁰, 39, F₃, 5) (dual of [39, 29, 6]-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(3¹²⁶, 913, F₃, 3, 25) (dual of [(913, 3), 2613, 26]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3¹²⁶, 913, F₃, 4, 25) (dual of [(913, 4), 3526, 26]-NRT-code)	[i]		OOA Folding