MinT - Information on Result #947883

Information on Result #947883

Linear OOA(2²⁴⁷, 2746, F₂, 3, 37) (dual of [(2746, 3), 7991, 38]-NRT-code), using OOA 3-folding based on linear OA(2²⁴⁷, 8238, F₂, 37) (dual of [8238, 7991, 38]-code), using

discarding factors / shortening the dual code based on linear OA(2²⁴⁷, 8240, F₂, 37) (dual of [8240, 7993, 38]-code), using
- constructionÂ X applied to C_e(36) âŠ‚ C_e(30) [i] based on
  1. linear OA(2²³⁵, 8192, F₂, 37) (dual of [8192, 7957, 38]-code), using an extension C_e(36) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,36], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [i]
  2. linear OA(2¹⁹⁶, 8192, F₂, 31) (dual of [8192, 7996, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [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(2²⁴⁷, 2166, F₂, 4, 37) (dual of [(2166, 4), 8417, 38]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁴⁷, 2166, F₂, 5, 37) (dual of [(2166, 5), 10583, 38]-NRT-code)	[i]
3	Linear OOA(2²⁴⁷, 2166, F₂, 6, 37) (dual of [(2166, 6), 12749, 38]-NRT-code)	[i]
4	Linear OOA(2²⁴⁷, 2166, F₂, 7, 37) (dual of [(2166, 7), 14915, 38]-NRT-code)	[i]
5	Linear OOA(2²⁴⁷, 2166, F₂, 8, 37) (dual of [(2166, 8), 17081, 38]-NRT-code)	[i]
6	Digital (210, 247, 2166)-net over F₂	[i]