Linear OA(2²⁵⁰, 621, F₂, 52) (dual of [621, 371, 53]-code), using 59 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, 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(2²²², 534, F₂, 52) (dual of [534, 312, 53]-code), using

• 1 times truncation [i] based on linear OA(2²²³, 535, F₂, 53) (dual of [535, 312, 54]-code), using
  • construction XX applied to C₁ = C([461,0]), C₂ = C([465,2]), C₃ = C₁ + C₂ = C([465,0]), and C_∩ = C₁ ∩ C₂ = C([461,2]) [i] based on
    1. linear OA(2²⁰⁸, 511, F₂, 51) (dual of [511, 303, 52]-code), using the primitive BCH-code C(I) with length 511 = 2⁹−1, defining interval I = {−50,−49,…,0}, and designed minimum distance d ≥ |I|+1 = 52 [i]
    2. linear OA(2²⁰⁸, 511, F₂, 49) (dual of [511, 303, 50]-code), using the primitive BCH-code C(I) with length 511 = 2⁹−1, defining interval I = {−46,−45,…,2}, and designed minimum distance d ≥ |I|+1 = 50 [i]
    3. 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 = {−50,−49,…,2}, and designed minimum distance d ≥ |I|+1 = 54 [i]
    4. linear OA(2¹⁹⁹, 511, F₂, 47) (dual of [511, 312, 48]-code), using the primitive BCH-code C(I) with length 511 = 2⁹−1, defining interval I = {−46,−45,…,0}, and designed minimum distance d ≥ |I|+1 = 48 [i]
    5. linear OA(2⁵, 14, F₂, 3) (dual of [14, 9, 4]-code or 14-cap in PG(4,2)), using
       • discarding factors / shortening the dual code based on linear OA(2⁵, 16, F₂, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), using
         • Reed–Muller code RM(1,4) [i]
         • caps in base b = 2 [i]
    6. 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]