MinT - Information on Result #1685744

Information on Result #1685744

Linear OOA(2²⁰⁹, 1362, F₂, 7, 34) (dual of [(1362, 7), 9325, 35]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁰⁹, 1362, F₂, 3, 34) (dual of [(1362, 3), 3877, 35]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁰⁹, 1370, F₂, 3, 34) (dual of [(1370, 3), 3901, 35]-NRT-code), using
- 2² times duplication [i] based on linear OOA(2²⁰⁷, 1370, F₂, 3, 34) (dual of [(1370, 3), 3903, 35]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2²⁰⁷, 4110, F₂, 34) (dual of [4110, 3903, 35]-code), using
    - 2 times code embedding in larger space [i] based on linear OA(2²⁰⁵, 4108, F₂, 34) (dual of [4108, 3903, 35]-code), using
      - 1 times truncation [i] based on linear OA(2²⁰⁶, 4109, F₂, 35) (dual of [4109, 3903, 36]-code), using
        constructionÂ X applied to C_e(34) âŠ‚ C_e(32) [i] based on
        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(2¹⁹³, 4096, F₂, 33) (dual of [4096, 3903, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [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.