MinT - Information on Result #2486250

Information on Result #2486250

Linear OOA(3¹⁴³, 265743, F₃, 2, 17) (dual of [(265743, 2), 531343, 18]-NRT-code), using 3¹ times duplication based on linear OOA(3¹⁴², 265743, F₃, 2, 17) (dual of [(265743, 2), 531344, 18]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(3¹⁴⁰, 265742, F₃, 2, 17) (dual of [(265742, 2), 531344, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁴⁰, 531484, F₃, 17) (dual of [531484, 531344, 18]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(3¹³⁹, 531483, F₃, 17) (dual of [531483, 531344, 18]-code), using
    - constructionÂ X applied to C_e(16) âŠ‚ C_e(12) [i] based on
      1. linear OA(3¹³³, 531441, F₃, 17) (dual of [531441, 531308, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
      2. 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]
      3. linear OA(3⁶, 42, F₃, 3) (dual of [42, 36, 4]-code or 42-cap in PG(5,3)), using
        discarding factors / shortening the dual code based on linear OA(3⁶, 48, F₃, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
        large caps in PG(5,Â b) [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(3¹⁴³, 193059, F₃, 3, 17) (dual of [(193059, 3), 579034, 18]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁴³, 193059, F₃, 4, 17) (dual of [(193059, 4), 772093, 18]-NRT-code)	[i]
3	Linear OOA(3¹⁴³, 193059, F₃, 5, 17) (dual of [(193059, 5), 965152, 18]-NRT-code)	[i]
4	Digital (126, 143, 193059)-net over F₃	[i]