MinT - Information on Result #1704803

Information on Result #1704803

Linear OOA(2²³³, 75065, F₂, 8, 24) (dual of [(75065, 8), 600287, 25]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²³³, 75065, F₂, 6, 24) (dual of [(75065, 6), 450157, 25]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²³³, 87385, F₂, 6, 24) (dual of [(87385, 6), 524077, 25]-NRT-code), using
- 2¹ times duplication [i] based on linear OOA(2²³², 87385, F₂, 6, 24) (dual of [(87385, 6), 524078, 25]-NRT-code), using
  - OOA 6-folding [i] based on linear OA(2²³², 524310, F₂, 24) (dual of [524310, 524078, 25]-code), using
    - 3 times code embedding in larger space [i] based on linear OA(2²²⁹, 524307, F₂, 24) (dual of [524307, 524078, 25]-code), using
      - 1 times truncation [i] 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, 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

None.