Linear OA(2²⁵², 587, F₂, 54) (dual of [587, 335, 55]-code), using 40 step VarÅ¡amov–Edel lengthening with (r_i) = (6, 3, 2, 1, 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, 0, 0, 0, 1, 4 times 0) based on linear OA(2²²⁶, 521, F₂, 54) (dual of [521, 295, 55]-code), using

• 1 times truncation [i] based on linear OA(2²²⁷, 522, F₂, 55) (dual of [522, 295, 56]-code), using
  • construction X applied to C_e(54) ⊂ C_e(52) [i] based on
    1. linear OA(2²²⁶, 512, F₂, 55) (dual of [512, 286, 56]-code), using an extension C_e(54) of the primitive narrow-sense BCH-code C(I) with length 511 = 2⁹−1, defining interval I = [1,54], and designed minimum distance d ≥ |I|+1 = 55 [i]
    2. linear OA(2²¹⁷, 512, F₂, 53) (dual of [512, 295, 54]-code), using an extension C_e(52) of the primitive narrow-sense BCH-code C(I) with length 511 = 2⁹−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53 [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]