MinT - Information on Result #1752631

Information on Result #1752631

Digital (137, 159, 3962)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁵⁹, 3962, F₂, 4, 22) (dual of [(3962, 4), 15689, 23]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁵⁹, 4100, F₂, 4, 22) (dual of [(4100, 4), 16241, 23]-NRT-code), using
- 2² times duplication [i] based on linear OOA(2¹⁵⁷, 4100, F₂, 4, 22) (dual of [(4100, 4), 16243, 23]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(2¹⁵⁷, 16400, F₂, 22) (dual of [16400, 16243, 23]-code), using
    - 2 times code embedding in larger space [i] based on linear OA(2¹⁵⁵, 16398, F₂, 22) (dual of [16398, 16243, 23]-code), using
      - 1 times truncation [i] based on linear OA(2¹⁵⁶, 16399, F₂, 23) (dual of [16399, 16243, 24]-code), using
        constructionÂ X applied to C_e(22) âŠ‚ C_e(20) [i] based on
        linear OA(2¹⁵⁵, 16384, F₂, 23) (dual of [16384, 16229, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
        linear OA(2¹⁴¹, 16384, F₂, 21) (dual of [16384, 16243, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
        linear OA(2¹, 15, F₂, 1) (dual of [15, 14, 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, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.