MinT - Information on Result #1685172

Information on Result #1685172

Linear OOA(2²⁰¹, 1977, F₂, 7, 31) (dual of [(1977, 7), 13638, 32]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁰¹, 1977, F₂, 4, 31) (dual of [(1977, 4), 7707, 32]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁰¹, 2052, F₂, 4, 31) (dual of [(2052, 4), 8007, 32]-NRT-code), using
- 2² times duplication [i] based on linear OOA(2¹⁹⁹, 2052, F₂, 4, 31) (dual of [(2052, 4), 8009, 32]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(2¹⁹⁹, 8208, F₂, 31) (dual of [8208, 8009, 32]-code), using
    - 2 times code embedding in larger space [i] based on linear OA(2¹⁹⁷, 8206, F₂, 31) (dual of [8206, 8009, 32]-code), using
      - constructionÂ X applied to C_e(30) âŠ‚ C_e(28) [i] based on
        linear OA(2¹⁹⁶, 8192, F₂, 31) (dual of [8192, 7996, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
        linear OA(2¹⁸³, 8192, F₂, 29) (dual of [8192, 8009, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
        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

None.