MinT - Information on Result #1653596

Information on Result #1653596

Linear OOA(2²³⁶, 1677767, F₂, 5, 19) (dual of [(1677767, 5), 8388599, 20]-NRT-code), using (u,Â u+v)-construction based on

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]
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.

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