MinT - Information on Result #2788264

Information on Result #2788264

Linear OOA(2¹¹⁹, 2097151, F₂, 4, 11) (dual of [(2097151, 4), 8388485, 12]-NRT-code), using 2¹ times duplication based on linear OOA(2¹¹⁸, 2097151, F₂, 4, 11) (dual of [(2097151, 4), 8388486, 12]-NRT-code), using

OOA 2-folding [i] based on linear OOA(2¹¹⁸, 4194302, F₂, 2, 11) (dual of [(4194302, 2), 8388486, 12]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2¹¹⁶, 4194301, F₂, 2, 11) (dual of [(4194301, 2), 8388486, 12]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2¹¹⁶, 8388602, F₂, 11) (dual of [8388602, 8388486, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹¹⁶, large, F₂, 11) (dual of [large, large−116, 12]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(2¹¹⁹, 1761821, F₂, 5, 11) (dual of [(1761821, 5), 8808986, 12]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹¹⁹, 1761821, F₂, 6, 11) (dual of [(1761821, 6), 10570807, 12]-NRT-code)	[i]
3	Linear OOA(2¹¹⁹, 1761821, F₂, 7, 11) (dual of [(1761821, 7), 12332628, 12]-NRT-code)	[i]
4	Linear OOA(2¹¹⁹, 1761821, F₂, 8, 11) (dual of [(1761821, 8), 14094449, 12]-NRT-code)	[i]
5	Digital (108, 119, 1761821)-net over F₂	[i]