MinT - Information on Result #1630830

Information on Result #1630830

Linear OOA(2⁹⁹, 14128, F₂, 5, 13) (dual of [(14128, 5), 70541, 14]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2⁹⁹, 14128, F₂, 4, 13) (dual of [(14128, 4), 56413, 14]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2⁹⁹, 16388, F₂, 4, 13) (dual of [(16388, 4), 65453, 14]-NRT-code), using
- 2¹ times duplication [i] based on linear OOA(2⁹⁸, 16388, F₂, 4, 13) (dual of [(16388, 4), 65454, 14]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(2⁹⁸, 65552, F₂, 13) (dual of [65552, 65454, 14]-code), using
    - discarding factors / shortening the dual code based on linear OA(2⁹⁸, 65553, F₂, 13) (dual of [65553, 65455, 14]-code), using
      - constructionÂ X applied to C_e(12) âŠ‚ C_e(10) [i] based on
        linear OA(2⁹⁷, 65536, F₂, 13) (dual of [65536, 65439, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(2⁸¹, 65536, F₂, 11) (dual of [65536, 65455, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(2¹, 17, F₂, 1) (dual of [17, 16, 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.