MinT - Information on Result #1639484

Information on Result #1639484

Linear OOA(2²⁴⁸, 2051, F₂, 5, 38) (dual of [(2051, 5), 10007, 39]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁴⁸, 2051, F₂, 4, 38) (dual of [(2051, 4), 7956, 39]-NRT-code), using

OOA 4-folding [i] 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: 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		This result only	Method
1	Linear OOA(2²⁴⁹, 2051, F₂, 5, 38) (dual of [(2051, 5), 10006, 39]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2²⁵⁰, 2051, F₂, 5, 38) (dual of [(2051, 5), 10005, 39]-NRT-code)	[i]		OOA Duplication