MinT - Information on Result #1297767

Information on Result #1297767

Linear OA(2²⁵⁶, 465, F₂, 62) (dual of [465, 209, 63]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(2²⁵⁰, 454, F₂, 62) (dual of [454, 204, 63]-code), using
- 1 times truncation [i] based on linear OA(2²⁵¹, 455, F₂, 63) (dual of [455, 204, 64]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(64³¹, 65, F₆₄, 31) (dual of [65, 34, 32]-code or 65-arc in PG(30,64)), using
      - extended Reedâ€“Solomon code RS_e(34,64) [i]
      - the expurgated narrow-sense BCH-code C(I) with length 65Â | 64²âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]
    2. linear OA(2¹, 7, F₂, 1) (dual of [7, 6, 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]
linear OA(2²⁵⁰, 459, F₂, 60) (dual of [459, 209, 61]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 2²⁵⁰Â > V_b^sâˆ’1(kâˆ’1)Â = 1666 463259 547233 186402 249779 479856 816860 504928 180954 375417 650540 914095 382272 [i]
linear OA(2¹, 6, F₂, 1) (dual of [6, 5, 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 (see above)

Mode: Linear.

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