MinT - Information on Result #2467792

Information on Result #2467792

Linear OOA(3¹⁵³, 265742, F₃, 2, 18) (dual of [(265742, 2), 531331, 19]-NRT-code), using 1 step truncation based on linear OOA(3¹⁵⁴, 265743, F₃, 2, 19) (dual of [(265743, 2), 531332, 20]-NRT-code), using

OOA 2-folding [i] based on linear OA(3¹⁵⁴, 531486, F₃, 19) (dual of [531486, 531332, 20]-code), using
- constructionÂ X applied to C_e(18) âŠ‚ C_e(13) [i] based on
  1. linear OA(3¹⁴⁵, 531441, F₃, 19) (dual of [531441, 531296, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
  2. 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]
  3. linear OA(3⁹, 45, F₃, 4) (dual of [45, 36, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁹, 80, F₃, 4) (dual of [80, 71, 5]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [0,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [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(3¹⁵³, 204046, F₃, 3, 18) (dual of [(204046, 3), 611985, 19]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁵³, 204046, F₃, 4, 18) (dual of [(204046, 4), 816031, 19]-NRT-code)	[i]
3	Linear OOA(3¹⁵³, 204046, F₃, 5, 18) (dual of [(204046, 5), 1020077, 19]-NRT-code)	[i]
4	Digital (135, 153, 204046)-net over F₃	[i]