MinT - Information on Result #1669350

Information on Result #1669350

Linear OOA(2²²¹, 1235, F₂, 6, 37) (dual of [(1235, 6), 7189, 38]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²²¹, 1235, F₂, 3, 37) (dual of [(1235, 3), 3484, 38]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²²¹, 1370, F₂, 3, 37) (dual of [(1370, 3), 3889, 38]-NRT-code), using
- 2² times duplication [i] based on linear OOA(2²¹⁹, 1370, F₂, 3, 37) (dual of [(1370, 3), 3891, 38]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2²¹⁹, 4110, F₂, 37) (dual of [4110, 3891, 38]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(2²¹⁸, 4109, F₂, 37) (dual of [4109, 3891, 38]-code), using
      - constructionÂ X applied to C_e(36) âŠ‚ C_e(34) [i] based on
        linear OA(2²¹⁷, 4096, F₂, 37) (dual of [4096, 3879, 38]-code), using an extension C_e(36) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,36], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [i]
        linear OA(2²⁰⁵, 4096, F₂, 35) (dual of [4096, 3891, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
        linear OA(2¹, 13, F₂, 1) (dual of [13, 12, 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.