MinT - Information on Result #1051604

Information on Result #1051604

Linear OOA(2¹²⁵, 32775, F₂, 4, 14) (dual of [(32775, 4), 130975, 15]-NRT-code), using OOA 4-folding based on linear OA(2¹²⁵, 131100, F₂, 14) (dual of [131100, 130975, 15]-code), using

discarding factors / shortening the dual code based on linear OA(2¹²⁵, 131103, F₂, 14) (dual of [131103, 130978, 15]-code), using
- 1 times truncation [i] based on linear OA(2¹²⁶, 131104, F₂, 15) (dual of [131104, 130978, 16]-code), using
  - constructionÂ X applied to C_e(14) âŠ‚ C_e(10) [i] based on
    1. linear OA(2¹²⁰, 131072, F₂, 15) (dual of [131072, 130952, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
    2. linear OA(2⁸⁶, 131072, F₂, 11) (dual of [131072, 130986, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
    3. linear OA(2⁶, 32, F₂, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
      - Reedâ€“Muller code RM(1,5) [i]
      - caps in base bÂ =Â 2 [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(2¹²⁵, 32775, F₂, 5, 14) (dual of [(32775, 5), 163750, 15]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹²⁵, 32775, F₂, 6, 14) (dual of [(32775, 6), 196525, 15]-NRT-code)	[i]
3	Linear OOA(2¹²⁵, 32775, F₂, 7, 14) (dual of [(32775, 7), 229300, 15]-NRT-code)	[i]
4	Linear OOA(2¹²⁵, 32775, F₂, 8, 14) (dual of [(32775, 8), 262075, 15]-NRT-code)	[i]
5	Digital (111, 125, 32775)-net over F₂	[i]