MinT - Information on Result #1670420

Information on Result #1670420

Linear OOA(2²³⁵, 1677767, F₂, 6, 18) (dual of [(1677767, 6), 10066367, 19]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²³⁵, 1677767, F₂, 5, 18) (dual of [(1677767, 5), 8388600, 19]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2²⁸, 47, F₂, 5, 9) (dual of [(47, 5), 207, 10]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2²⁸, 47, F₂, 2, 9) (dual of [(47, 2), 66, 10]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2²⁸, 94, F₂, 9) (dual of [94, 66, 10]-code), using
      - discarding factors / shortening the dual code based on linear OA(2²⁸, 95, F₂, 9) (dual of [95, 67, 10]-code), using
        adding a parity check bit [i] based on linear OA(2²⁷, 94, F₂, 8) (dual of [94, 67, 9]-code), using
        a â€œGraâ€ code from Grasslâ€™s database [i]
2. linear OOA(2²⁰⁷, 1677720, F₂, 5, 18) (dual of [(1677720, 5), 8388393, 19]-NRT-code), using
  - OOA 5-folding [i] based on linear OA(2²⁰⁷, 8388600, F₂, 18) (dual of [8388600, 8388393, 19]-code), using
    - discarding factors / shortening the dual code based on linear OA(2²⁰⁷, large, F₂, 18) (dual of [large, large−207, 19]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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.