Linear OA(2²²⁴, 586, F₂, 46) (dual of [586, 362, 47]-code), using 40 step VarÅ¡amov–Edel lengthening with (r_i) = (6, 3, 2, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0) based on linear OA(2¹⁹⁹, 521, F₂, 46) (dual of [521, 322, 47]-code), using

• 1 times truncation [i] based on linear OA(2²⁰⁰, 522, F₂, 47) (dual of [522, 322, 48]-code), using
  • construction X applied to C_e(46) ⊂ C_e(44) [i] based on
    1. linear OA(2¹⁹⁹, 512, F₂, 47) (dual of [512, 313, 48]-code), using an extension C_e(46) of the primitive narrow-sense BCH-code C(I) with length 511 = 2⁹−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
    2. linear OA(2¹⁹⁰, 512, F₂, 45) (dual of [512, 322, 46]-code), using an extension C_e(44) of the primitive narrow-sense BCH-code C(I) with length 511 = 2⁹−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
    3. linear OA(2¹, 10, F₂, 1) (dual of [10, 9, 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]