Linear OA(2²⁵⁷, 622, F₂, 54) (dual of [622, 365, 55]-code), using 62 step VarÅ¡amov–Edel lengthening with (r_i) = (6, 3, 2, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0) based on linear OA(2²²⁷, 530, F₂, 54) (dual of [530, 303, 55]-code), using

• 1 times truncation [i] based on linear OA(2²²⁸, 531, F₂, 55) (dual of [531, 303, 56]-code), using
  • construction XX applied to C₁ = C([509,50]), C₂ = C([0,52]), C₃ = C₁ + C₂ = C([0,50]), and C_∩ = C₁ ∩ C₂ = C([509,52]) [i] based on
    1. linear OA(2²¹⁷, 511, F₂, 53) (dual of [511, 294, 54]-code), using the primitive BCH-code C(I) with length 511 = 2⁹−1, defining interval I = {−2,−1,…,50}, and designed minimum distance d ≥ |I|+1 = 54 [i]
    2. linear OA(2²¹⁷, 511, F₂, 53) (dual of [511, 294, 54]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 2⁹−1, defining interval I = [0,52], and designed minimum distance d ≥ |I|+1 = 54 [i]
    3. linear OA(2²²⁶, 511, F₂, 55) (dual of [511, 285, 56]-code), using the primitive BCH-code C(I) with length 511 = 2⁹−1, defining interval I = {−2,−1,…,52}, and designed minimum distance d ≥ |I|+1 = 56 [i]
    4. linear OA(2²⁰⁸, 511, F₂, 51) (dual of [511, 303, 52]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 2⁹−1, defining interval I = [0,50], and designed minimum distance d ≥ |I|+1 = 52 [i]
    5. 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]
    6. linear OA(2¹, 10, F₂, 1) (dual of [10, 9, 2]-code) (see above)