MinT - Information on Result #1054405

Information on Result #1054405

Linear OOA(2²⁴⁸, 2051, F₂, 4, 38) (dual of [(2051, 4), 7956, 39]-NRT-code), using OOA 4-folding based on linear OA(2²⁴⁸, 8204, F₂, 38) (dual of [8204, 7956, 39]-code), using

discarding factors / shortening the dual code based on linear OA(2²⁴⁸, 8205, F₂, 38) (dual of [8205, 7957, 39]-code), using
- 1 times truncation [i] based on linear OA(2²⁴⁹, 8206, F₂, 39) (dual of [8206, 7957, 40]-code), using
  - constructionÂ X applied to C_e(38) âŠ‚ C_e(36) [i] based on
    1. linear OA(2²⁴⁸, 8192, F₂, 39) (dual of [8192, 7944, 40]-code), using an extension C_e(38) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,38], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [i]
    2. 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]
    3. linear OA(2¹, 14, F₂, 1) (dual of [14, 13, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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(2²⁴⁸, 2051, F₂, 5, 38) (dual of [(2051, 5), 10007, 39]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁴⁸, 2051, F₂, 6, 38) (dual of [(2051, 6), 12058, 39]-NRT-code)	[i]
3	Linear OOA(2²⁴⁸, 2051, F₂, 7, 38) (dual of [(2051, 7), 14109, 39]-NRT-code)	[i]
4	Linear OOA(2²⁴⁸, 2051, F₂, 8, 38) (dual of [(2051, 8), 16160, 39]-NRT-code)	[i]
5	Digital (210, 248, 2051)-net over F₂	[i]