Information on Result #701101
Linear OA(456, 73, F4, 31) (dual of [73, 17, 32]-code), using construction XX applied to C1 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,47}), C2 = C([1,27]), C3 = C1 + C2 = C([1,26]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,47}) based on
- linear OA(450, 63, F4, 28) (dual of [63, 13, 29]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,47}, and minimum distance d ≥ |{−1,0,…,26}|+1 = 29 (BCH-bound) [i]
- linear OA(449, 63, F4, 29) (dual of [63, 14, 30]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 30 [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 = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,47}, and minimum distance d ≥ |{−1,0,…,29}|+1 = 32 (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(41, 5, F4, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(42, 5, F4, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,4)), using
- extended Reed–Solomon code RSe(3,4) [i]
- Hamming code H(2,4) [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.