Information on Result #701180
Linear OA(525, 35, F5, 15) (dual of [35, 10, 16]-code), using construction XX applied to C1 = C({0,1,2,3,4,6,7,8,14,19}), C2 = C([0,9]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,6,7,8,9,14,19}) based on
- linear OA(518, 24, F5, 11) (dual of [24, 6, 12]-code), using the primitive cyclic code C(A) with length 24 = 52−1, defining set A = {0,1,2,3,4,6,7,8,14,19}, and minimum distance d ≥ |{−2,−1,…,8}|+1 = 12 (BCH-bound) [i]
- linear OA(516, 24, F5, 12) (dual of [24, 8, 13]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(520, 24, F5, 17) (dual of [24, 4, 18]-code), using the primitive cyclic code C(A) with length 24 = 52−1, defining set A = {0,1,2,3,4,6,7,8,9,14,19}, and minimum distance d ≥ |{−5,−4,…,11}|+1 = 18 (BCH-bound) [i]
- linear OA(514, 24, F5, 9) (dual of [24, 10, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(52, 6, F5, 2) (dual of [6, 4, 3]-code or 6-arc in PG(1,5)), using
- extended Reed–Solomon code RSe(4,5) [i]
- Hamming code H(2,5) [i]
- linear OA(53, 5, F5, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,5) or 5-cap in PG(2,5)), using
- Reed–Solomon code RS(2,5) [i]
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
None.