Information on Result #701089
Linear OA(458, 77, F4, 31) (dual of [77, 19, 32]-code), using construction XX applied to C1 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,31,47}), C2 = C([1,26]), C3 = C1 + C2 = C([1,23]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,31,47}) based on
- linear OA(450, 63, F4, 30) (dual of [63, 13, 31]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,31,47}, and minimum distance d ≥ |{−4,−3,…,25}|+1 = 31 (BCH-bound) [i]
- linear OA(446, 63, F4, 26) (dual of [63, 17, 27]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(453, 63, F4, 31) (dual of [63, 10, 32]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,31,47}, and minimum distance d ≥ |{−4,−3,…,26}|+1 = 32 (BCH-bound) [i]
- linear OA(443, 63, F4, 25) (dual of [63, 20, 26]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 26 [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.