MinT - Information on Result #2480410

Information on Result #2480410

Linear OOA(2²¹⁹, 1039, F₂, 2, 39) (dual of [(1039, 2), 1859, 40]-NRT-code), using 2¹ times duplication based on linear OOA(2²¹⁸, 1039, F₂, 2, 39) (dual of [(1039, 2), 1860, 40]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(2²¹⁶, 1038, F₂, 2, 39) (dual of [(1038, 2), 1860, 40]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2²¹⁶, 2076, F₂, 39) (dual of [2076, 1860, 40]-code), using
  - constructionÂ X applied to C_e(38) âŠ‚ C_e(34) [i] based on
    1. 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]
    2. linear OA(2¹⁸⁸, 2048, F₂, 35) (dual of [2048, 1860, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [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(2²¹⁹, 880, F₂, 3, 39) (dual of [(880, 3), 2421, 40]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²¹⁹, 880, F₂, 4, 39) (dual of [(880, 4), 3301, 40]-NRT-code)	[i]
3	Linear OOA(2²¹⁹, 880, F₂, 5, 39) (dual of [(880, 5), 4181, 40]-NRT-code)	[i]
4	Linear OOA(2²¹⁹, 880, F₂, 6, 39) (dual of [(880, 6), 5061, 40]-NRT-code)	[i]
5	Linear OOA(2²¹⁹, 880, F₂, 7, 39) (dual of [(880, 7), 5941, 40]-NRT-code)	[i]
6	Linear OOA(2²¹⁹, 880, F₂, 8, 39) (dual of [(880, 8), 6821, 40]-NRT-code)	[i]
7	Digital (180, 219, 880)-net over F₂	[i]