MinT - Information on Result #1672286

Information on Result #1672286

Linear OOA(2²⁵⁷, 1679085, F₂, 6, 19) (dual of [(1679085, 6), 10074253, 20]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁵⁷, 1679085, F₂, 5, 19) (dual of [(1679085, 5), 8395168, 20]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁴⁹, 1365, F₂, 5, 9) (dual of [(1365, 5), 6776, 10]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2⁴⁹, 1365, F₂, 3, 9) (dual of [(1365, 3), 4046, 10]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(2⁴⁹, 4095, F₂, 9) (dual of [4095, 4046, 10]-code), using
      - discarding factors / shortening the dual code based on linear OA(2⁴⁹, 4096, F₂, 9) (dual of [4096, 4047, 10]-code), using
        an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
2. linear OOA(2²⁰⁸, 1677720, F₂, 5, 19) (dual of [(1677720, 5), 8388392, 20]-NRT-code), using
  - OOA 5-folding [i] based on linear OA(2²⁰⁸, 8388600, F₂, 19) (dual of [8388600, 8388392, 20]-code), using
    - discarding factors / shortening the dual code based on linear OA(2²⁰⁸, large, F₂, 19) (dual of [large, large−208, 20]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]

Mode: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.