Linear OA(49⁵⁵, 68, F₄₉, 47) (dual of [68, 13, 48]-code), using construction XX applied to C₁ = C({0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,21,23,24}), C₂ = C([0,19]), C₃ = C₁ + C₂ = C([0,18]), and C_∩ = C₁ ∩ C₂ = C({0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,23,24}) based on

1. linear OA(49⁴⁵, 50, F₄₉, 45) (dual of [50, 5, 46]-code or 50-arc in PG(44,49)), using the cyclic code C(A) with length 50 | 49²âˆ’1, defining set A = {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,21,23,24}, and minimum distance d ≥ |{−16,−13,−10,…,16}|+1 = 46 (BCH-bound) [i]
2. linear OA(49³⁹, 50, F₄₉, 39) (dual of [50, 11, 40]-code or 50-arc in PG(38,49)), using the expurgated narrow-sense BCH-code C(I) with length 50 | 49²âˆ’1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (BCH-bound) [i]
3. linear OA(49⁴⁷, 50, F₄₉, 47) (dual of [50, 3, 48]-code or 50-arc in PG(46,49)), using the cyclic code C(A) with length 50 | 49²âˆ’1, defining set A = {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,23,24}, and minimum distance d ≥ |{−19,−16,−13,…,19}|+1 = 48 (BCH-bound) [i]
4. linear OA(49³⁷, 50, F₄₉, 37) (dual of [50, 13, 38]-code or 50-arc in PG(36,49)), using the expurgated narrow-sense BCH-code C(I) with length 50 | 49²âˆ’1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
5. linear OA(49⁷, 15, F₄₉, 7) (dual of [15, 8, 8]-code or 15-arc in PG(6,49)), using
   • discarding factors / shortening the dual code based on linear OA(49⁷, 49, F₄₉, 7) (dual of [49, 42, 8]-code or 49-arc in PG(6,49)), using
     • Reed–Solomon code RS(42,49) [i]
6. linear OA(49¹, 3, F₄₉, 1) (dual of [3, 2, 2]-code), using
   • discarding factors / shortening the dual code based on linear OA(49¹, 49, F₄₉, 1) (dual of [49, 48, 2]-code), using
     • Reed–Solomon code RS(48,49) [i]