MinT - Information on Result #812621

Information on Result #812621

Linear OOA(3⁵¹, 265728, F₃, 2, 7) (dual of [(265728, 2), 531405, 8]-NRT-code), using OOA 2-folding based on linear OA(3⁵¹, 531456, F₃, 7) (dual of [531456, 531405, 8]-code), using

1 times code embedding in larger space [i] based on linear OA(3⁵⁰, 531455, F₃, 7) (dual of [531455, 531405, 8]-code), using
- constructionÂ X4 applied to C_e(6) âŠ‚ C_e(4) [i] based on
  1. linear OA(3⁴⁹, 531441, F₃, 7) (dual of [531441, 531392, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
  2. linear OA(3³⁷, 531441, F₃, 5) (dual of [531441, 531404, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
  3. linear OA(3¹³, 14, F₃, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,3)), using
    - dual of repetition code with length 14 [i]
  4. linear OA(3¹, 14, F₃, 1) (dual of [14, 13, 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(3⁵², 265728, F₃, 2, 7) (dual of [(265728, 2), 531404, 8]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3⁵¹, 265728, F₃, 3, 7) (dual of [(265728, 3), 797133, 8]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(3⁵¹, 265728, F₃, 4, 7) (dual of [(265728, 4), 1062861, 8]-NRT-code)	[i]
4	Linear OOA(3⁵¹, 265728, F₃, 5, 7) (dual of [(265728, 5), 1328589, 8]-NRT-code)	[i]
5	Digital (44, 51, 265728)-net over F₃	[i]