MinT - Information on Result #2480630

Information on Result #2480630

Linear OOA(2²³⁹, 1038, F₂, 2, 42) (dual of [(1038, 2), 1837, 43]-NRT-code), using 2¹ times duplication based on linear OOA(2²³⁸, 1038, F₂, 2, 42) (dual of [(1038, 2), 1838, 43]-NRT-code), using

OOA 2-folding [i] based on linear OA(2²³⁸, 2076, F₂, 42) (dual of [2076, 1838, 43]-code), using
- strength reduction [i] based on linear OA(2²³⁸, 2076, F₂, 43) (dual of [2076, 1838, 44]-code), using
  - constructionÂ X applied to C_e(42) âŠ‚ C_e(38) [i] based on
    1. linear OA(2²³², 2048, F₂, 43) (dual of [2048, 1816, 44]-code), using an extension C_e(42) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,42], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 43 [i]
    2. linear OA(2²¹⁰, 2048, F₂, 39) (dual of [2048, 1838, 40]-code), using an extension C_e(38) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,38], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [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(2²³⁹, 984, F₂, 3, 42) (dual of [(984, 3), 2713, 43]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²³⁹, 984, F₂, 4, 42) (dual of [(984, 4), 3697, 43]-NRT-code)	[i]
3	Linear OOA(2²³⁹, 984, F₂, 5, 42) (dual of [(984, 5), 4681, 43]-NRT-code)	[i]
4	Linear OOA(2²³⁹, 984, F₂, 6, 42) (dual of [(984, 6), 5665, 43]-NRT-code)	[i]
5	Linear OOA(2²³⁹, 984, F₂, 7, 42) (dual of [(984, 7), 6649, 43]-NRT-code)	[i]
6	Linear OOA(2²³⁹, 984, F₂, 8, 42) (dual of [(984, 8), 7633, 43]-NRT-code)	[i]
7	Digital (197, 239, 984)-net over F₂	[i]