MinT - Information on Result #2486051

Information on Result #2486051

Linear OOA(3¹²⁵, 265735, F₃, 2, 15) (dual of [(265735, 2), 531345, 16]-NRT-code), using 3¹ times duplication based on linear OOA(3¹²⁴, 265735, F₃, 2, 15) (dual of [(265735, 2), 531346, 16]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(3¹²², 265734, F₃, 2, 15) (dual of [(265734, 2), 531346, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹²², 531468, F₃, 15) (dual of [531468, 531346, 16]-code), using
  - constructionÂ X4 applied to C([0,7]) âŠ‚ C([0,6]) [i] based on
    1. linear OA(3¹²¹, 531442, F₃, 15) (dual of [531442, 531321, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 3²⁴âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
    2. linear OA(3⁹⁷, 531442, F₃, 13) (dual of [531442, 531345, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 3²⁴âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
    3. linear OA(3²⁵, 26, F₃, 25) (dual of [26, 1, 26]-code or 26-arc in PG(24,3)), using
      - dual of repetition code with length 26 [i]
    4. linear OA(3¹, 26, F₃, 1) (dual of [26, 25, 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]

Mode: Constructive and 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		Method
1	Linear OOA(3¹²⁵, 205495, F₃, 3, 15) (dual of [(205495, 3), 616360, 16]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹²⁵, 205495, F₃, 4, 15) (dual of [(205495, 4), 821855, 16]-NRT-code)	[i]
3	Linear OOA(3¹²⁵, 205495, F₃, 5, 15) (dual of [(205495, 5), 1027350, 16]-NRT-code)	[i]
4	Digital (110, 125, 205495)-net over F₃	[i]