MinT - Information on Result #952400

Information on Result #952400

Linear OOA(3¹²⁸, 1594328, F₃, 3, 14) (dual of [(1594328, 3), 4782856, 15]-NRT-code), using OOA 3-folding based on linear OA(3¹²⁸, 4782984, F₃, 14) (dual of [4782984, 4782856, 15]-code), using

discarding factors / shortening the dual code based on linear OA(3¹²⁸, 4782985, F₃, 14) (dual of [4782985, 4782857, 15]-code), using
- constructionÂ X4 applied to C_e(13) âŠ‚ C_e(12) [i] based on
  1. linear OA(3¹²⁷, 4782969, F₃, 14) (dual of [4782969, 4782842, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
  2. linear OA(3¹¹³, 4782969, F₃, 13) (dual of [4782969, 4782856, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
  3. linear OA(3¹⁵, 16, F₃, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,3)), using
    - dual of repetition code with length 16 [i]
  4. linear OA(3¹, 16, F₃, 1) (dual of [16, 15, 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(3¹²⁹, 1594328, F₃, 3, 14) (dual of [(1594328, 3), 4782855, 15]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3¹²⁸, 1594328, F₃, 4, 14) (dual of [(1594328, 4), 6377184, 15]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(3¹²⁸, 1594328, F₃, 5, 14) (dual of [(1594328, 5), 7971512, 15]-NRT-code)	[i]
4	Digital (114, 128, 1594328)-net over F₃	[i]