Linear OA(2²⁶⁰, 595, F₂, 56) (dual of [595, 335, 57]-code), using 41 step VarÅ¡amov–Edel lengthening with (r_i) = (5, 3, 2, 1, 1, 1, 1, 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) based on linear OA(2²³⁶, 530, F₂, 56) (dual of [530, 294, 57]-code), using

• 1 times truncation [i] based on linear OA(2²³⁷, 531, F₂, 57) (dual of [531, 294, 58]-code), using
  • construction XX applied to C₁ = C([509,52]), C₂ = C([0,54]), C₃ = C₁ + C₂ = C([0,52]), and C_∩ = C₁ ∩ C₂ = C([509,54]) [i] based on
    1. 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]
    2. linear OA(2²²⁶, 511, F₂, 55) (dual of [511, 285, 56]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 2⁹−1, defining interval I = [0,54], and designed minimum distance d ≥ |I|+1 = 56 [i]
    3. linear OA(2²³⁵, 511, F₂, 57) (dual of [511, 276, 58]-code), using the primitive BCH-code C(I) with length 511 = 2⁹−1, defining interval I = {−2,−1,…,54}, and designed minimum distance d ≥ |I|+1 = 58 [i]
    4. 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]
    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)