MinT - Information on Result #2478969

Information on Result #2478969

Linear OOA(2¹²⁹, 1038, F₂, 2, 22) (dual of [(1038, 2), 1947, 23]-NRT-code), using 2¹ times duplication based on linear OOA(2¹²⁸, 1038, F₂, 2, 22) (dual of [(1038, 2), 1948, 23]-NRT-code), using

OOA 2-folding [i] based on linear OA(2¹²⁸, 2076, F₂, 22) (dual of [2076, 1948, 23]-code), using
- strength reduction [i] based on linear OA(2¹²⁸, 2076, F₂, 23) (dual of [2076, 1948, 24]-code), using
  - constructionÂ X applied to C_e(22) âŠ‚ C_e(18) [i] based on
    1. linear OA(2¹²², 2048, F₂, 23) (dual of [2048, 1926, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
    2. linear OA(2¹⁰⁰, 2048, F₂, 19) (dual of [2048, 1948, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    3. linear OA(2⁶, 28, F₂, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,2)), using
      - discarding factors / shortening the dual code based on 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(2¹²⁹, 788, F₂, 3, 22) (dual of [(788, 3), 2235, 23]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹²⁹, 788, F₂, 4, 22) (dual of [(788, 4), 3023, 23]-NRT-code)	[i]
3	Linear OOA(2¹²⁹, 788, F₂, 5, 22) (dual of [(788, 5), 3811, 23]-NRT-code)	[i]
4	Linear OOA(2¹²⁹, 788, F₂, 6, 22) (dual of [(788, 6), 4599, 23]-NRT-code)	[i]
5	Linear OOA(2¹²⁹, 788, F₂, 7, 22) (dual of [(788, 7), 5387, 23]-NRT-code)	[i]
6	Linear OOA(2¹²⁹, 788, F₂, 8, 22) (dual of [(788, 8), 6175, 23]-NRT-code)	[i]
7	Digital (107, 129, 788)-net over F₂	[i]