MinT - Information on Result #812939

Information on Result #812939

Linear OOA(3⁹⁹, 265734, F₃, 2, 12) (dual of [(265734, 2), 531369, 13]-NRT-code), using OOA 2-folding based on linear OA(3⁹⁹, 531468, F₃, 12) (dual of [531468, 531369, 13]-code), using

1 times code embedding in larger space [i] based on linear OA(3⁹⁸, 531467, F₃, 12) (dual of [531467, 531369, 13]-code), using
- constructionÂ X4 applied to C_e(12) âŠ‚ C_e(9) [i] based on
  1. linear OA(3⁹⁷, 531441, F₃, 13) (dual of [531441, 531344, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
  2. linear OA(3⁷³, 531441, F₃, 10) (dual of [531441, 531368, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [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(3¹⁰¹, 265735, F₃, 2, 12) (dual of [(265735, 2), 531369, 13]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(3¹⁰⁰, 265734, F₃, 2, 12) (dual of [(265734, 2), 531368, 13]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(3⁹⁹, 265734, F₃, 3, 12) (dual of [(265734, 3), 797103, 13]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(3⁹⁹, 265734, F₃, 4, 12) (dual of [(265734, 4), 1062837, 13]-NRT-code)	[i]
5	Linear OOA(3⁹⁹, 265734, F₃, 5, 12) (dual of [(265734, 5), 1328571, 13]-NRT-code)	[i]
6	Digital (87, 99, 265734)-net over F₃	[i]