MinT - Information on Result #2479582

Information on Result #2479582

Linear OOA(2¹⁶³, 1039, F₂, 2, 29) (dual of [(1039, 2), 1915, 30]-NRT-code), using 2¹ times duplication based on linear OOA(2¹⁶², 1039, F₂, 2, 29) (dual of [(1039, 2), 1916, 30]-NRT-code), using

OOA 2-folding [i] based on linear OA(2¹⁶², 2078, F₂, 29) (dual of [2078, 1916, 30]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2¹⁶¹, 2077, F₂, 29) (dual of [2077, 1916, 30]-code), using
  - constructionÂ X applied to C([0,14]) âŠ‚ C([0,12]) [i] based on
    1. linear OA(2¹⁵⁵, 2049, F₂, 29) (dual of [2049, 1894, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049Â | 2²²âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]
    2. linear OA(2¹³³, 2049, F₂, 25) (dual of [2049, 1916, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049Â | 2²²âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [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(2¹⁶³, 735, F₂, 3, 29) (dual of [(735, 3), 2042, 30]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁶³, 735, F₂, 4, 29) (dual of [(735, 4), 2777, 30]-NRT-code)	[i]
3	Linear OOA(2¹⁶³, 735, F₂, 5, 29) (dual of [(735, 5), 3512, 30]-NRT-code)	[i]
4	Linear OOA(2¹⁶³, 735, F₂, 6, 29) (dual of [(735, 6), 4247, 30]-NRT-code)	[i]
5	Linear OOA(2¹⁶³, 735, F₂, 7, 29) (dual of [(735, 7), 4982, 30]-NRT-code)	[i]
6	Linear OOA(2¹⁶³, 735, F₂, 8, 29) (dual of [(735, 8), 5717, 30]-NRT-code)	[i]
7	Digital (134, 163, 735)-net over F₂	[i]