MinT - Information on Result #808428

Information on Result #808428

Linear OOA(2²⁴⁰, 2071, F₂, 2, 38) (dual of [(2071, 2), 3902, 39]-NRT-code), using OOA 2-folding based on linear OA(2²⁴⁰, 4142, F₂, 38) (dual of [4142, 3902, 39]-code), using

discarding factors / shortening the dual code based on linear OA(2²⁴⁰, 4143, F₂, 38) (dual of [4143, 3903, 39]-code), using
- 1 times truncation [i] based on linear OA(2²⁴¹, 4144, F₂, 39) (dual of [4144, 3903, 40]-code), using
  - constructionÂ X applied to C_e(38) âŠ‚ C_e(32) [i] based on
    1. linear OA(2²²⁹, 4096, F₂, 39) (dual of [4096, 3867, 40]-code), using an extension C_e(38) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,38], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [i]
    2. linear OA(2¹⁹³, 4096, F₂, 33) (dual of [4096, 3903, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
    3. linear OA(2¹², 48, F₂, 5) (dual of [48, 36, 6]-code), using
      - adding a parity check bit [i] based on linear OA(2¹¹, 47, F₂, 4) (dual of [47, 36, 5]-code), using
        extracting embedded orthogonal array [i] based on digital (7, 11, 47)-net over F₂, using
        linear code embedding found in a computer search [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(2²⁴⁰, 1499, F₂, 3, 38) (dual of [(1499, 3), 4257, 39]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁴⁰, 1499, F₂, 4, 38) (dual of [(1499, 4), 5756, 39]-NRT-code)	[i]
3	Linear OOA(2²⁴⁰, 1499, F₂, 5, 38) (dual of [(1499, 5), 7255, 39]-NRT-code)	[i]
4	Linear OOA(2²⁴⁰, 1499, F₂, 6, 38) (dual of [(1499, 6), 8754, 39]-NRT-code)	[i]
5	Linear OOA(2²⁴⁰, 1499, F₂, 7, 38) (dual of [(1499, 7), 10253, 39]-NRT-code)	[i]
6	Linear OOA(2²⁴⁰, 1499, F₂, 8, 38) (dual of [(1499, 8), 11752, 39]-NRT-code)	[i]
7	Digital (202, 240, 1499)-net over F₂	[i]