MinT - Information on Result #1522902

Information on Result #1522902

Linear OOA(3¹²⁴, 1657, F₃, 3, 25) (dual of [(1657, 3), 4847, 26]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3¹²⁴, 1657, F₃, 25) (dual of [1657, 1533, 26]-code), using

discarding factors / shortening the dual code based on linear OA(3¹²⁴, 2227, F₃, 25) (dual of [2227, 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(3¹¹, 39, F₃, 5) (dual of [39, 28, 6]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹¹, 40, F₃, 5) (dual of [40, 29, 6]-code), using
      - (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
        linear OA(3¹, 13, F₃, 1) (dual of [13, 12, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
        linear OA(3³, 13, F₃, 2) (dual of [13, 10, 3]-code), using
        Hamming code H(3,3) [i]
        linear OA(3⁷, 14, F₃, 5) (dual of [14, 7, 6]-code), using
        extended quadratic residue code Q_e(14,3) [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(3¹²⁴, 828, F₃, 5, 25) (dual of [(828, 5), 4016, 26]-NRT-code)	[i]		OOA Folding