Information on Result #701047
Linear OA(452, 77, F4, 27) (dual of [77, 25, 28]-code), using construction XX applied to C1 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,31,47}), C2 = C([1,22]), C3 = C1 + C2 = C([1,21]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,31,47}) based on
- linear OA(444, 63, F4, 26) (dual of [63, 19, 27]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,31,47}, and minimum distance d ≥ |{−4,−3,…,21}|+1 = 27 (BCH-bound) [i]
- linear OA(440, 63, F4, 22) (dual of [63, 23, 23]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(447, 63, F4, 27) (dual of [63, 16, 28]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,31,47}, and minimum distance d ≥ |{−4,−3,…,22}|+1 = 28 (BCH-bound) [i]
- linear OA(437, 63, F4, 21) (dual of [63, 26, 22]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(45, 11, F4, 4) (dual of [11, 6, 5]-code), using
- linear OA(40, 3, F4, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
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.