MinT - Information on Result #2479335

Information on Result #2479335

Linear OOA(2¹⁵², 1039, F₂, 2, 26) (dual of [(1039, 2), 1926, 27]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2¹⁵⁰, 1038, F₂, 2, 26) (dual of [(1038, 2), 1926, 27]-NRT-code), using

OOA 2-folding [i] based on linear OA(2¹⁵⁰, 2076, F₂, 26) (dual of [2076, 1926, 27]-code), using
- strength reduction [i] based on linear OA(2¹⁵⁰, 2076, F₂, 27) (dual of [2076, 1926, 28]-code), using
  - constructionÂ X applied to C_e(26) âŠ‚ C_e(22) [i] based on
    1. linear OA(2¹⁴⁴, 2048, F₂, 27) (dual of [2048, 1904, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
    2. 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]
    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(2¹⁵³, 1039, F₂, 2, 26) (dual of [(1039, 2), 1925, 27]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹⁵², 834, F₂, 3, 26) (dual of [(834, 3), 2350, 27]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(2¹⁵², 834, F₂, 4, 26) (dual of [(834, 4), 3184, 27]-NRT-code)	[i]
4	Linear OOA(2¹⁵², 834, F₂, 5, 26) (dual of [(834, 5), 4018, 27]-NRT-code)	[i]
5	Linear OOA(2¹⁵², 834, F₂, 6, 26) (dual of [(834, 6), 4852, 27]-NRT-code)	[i]
6	Linear OOA(2¹⁵², 834, F₂, 7, 26) (dual of [(834, 7), 5686, 27]-NRT-code)	[i]
7	Linear OOA(2¹⁵², 834, F₂, 8, 26) (dual of [(834, 8), 6520, 27]-NRT-code)	[i]
8	Digital (126, 152, 834)-net over F₂	[i]