MinT - Information on Result #1757749

Information on Result #1757749

Digital (207, 232, 69185)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²³², 69185, F₂, 7, 25) (dual of [(69185, 7), 484063, 26]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²³², 74901, F₂, 7, 25) (dual of [(74901, 7), 524075, 26]-NRT-code), using
- 2² times duplication [i] based on linear OOA(2²³⁰, 74901, F₂, 7, 25) (dual of [(74901, 7), 524077, 26]-NRT-code), using
  - OOA 7-folding [i] based on linear OA(2²³⁰, 524307, F₂, 25) (dual of [524307, 524077, 26]-code), using
    - discarding factors / shortening the dual code based on linear OA(2²³⁰, 524308, F₂, 25) (dual of [524308, 524078, 26]-code), using
      - constructionÂ X applied to C_e(24) âŠ‚ C_e(22) [i] based on
        linear OA(2²²⁹, 524288, F₂, 25) (dual of [524288, 524059, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
        linear OA(2²¹⁰, 524288, F₂, 23) (dual of [524288, 524078, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
        linear OA(2¹, 20, F₂, 1) (dual of [20, 19, 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.