MinT - Information on Result #2485931

Information on Result #2485931

Linear OOA(3¹¹⁷, 265742, F₃, 2, 14) (dual of [(265742, 2), 531367, 15]-NRT-code), using 3¹ times duplication based on linear OOA(3¹¹⁶, 265742, F₃, 2, 14) (dual of [(265742, 2), 531368, 15]-NRT-code), using

OOA 2-folding [i] based on linear OA(3¹¹⁶, 531484, F₃, 14) (dual of [531484, 531368, 15]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3¹¹⁵, 531483, F₃, 14) (dual of [531483, 531368, 15]-code), using
  - constructionÂ X applied to C_e(13) âŠ‚ C_e(9) [i] based on
    1. linear OA(3¹⁰⁹, 531441, F₃, 14) (dual of [531441, 531332, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [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(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(3¹¹⁷, 238810, F₃, 3, 14) (dual of [(238810, 3), 716313, 15]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹¹⁷, 238810, F₃, 4, 14) (dual of [(238810, 4), 955123, 15]-NRT-code)	[i]
3	Linear OOA(3¹¹⁷, 238810, F₃, 5, 14) (dual of [(238810, 5), 1193933, 15]-NRT-code)	[i]
4	Digital (103, 117, 238810)-net over F₃	[i]