Information on Result #683978
Linear OA(5104, 167, F5, 44) (dual of [167, 63, 45]-code), using construction XX applied to C1 = C([0,40]), C2 = C([1,42]), C3 = C1 + C2 = C([1,40]), and C∩ = C1 ∩ C2 = C([0,42]) based on
- linear OA(594, 156, F5, 42) (dual of [156, 62, 43]-code), using the expurgated narrow-sense BCH-code C(I) with length 156 | 54−1, defining interval I = [0,40], and minimum distance d ≥ |{−1,0,…,40}|+1 = 43 (BCH-bound) [i]
- linear OA(5101, 156, F5, 42) (dual of [156, 55, 43]-code), using the narrow-sense BCH-code C(I) with length 156 | 54−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(5102, 156, F5, 44) (dual of [156, 54, 45]-code), using the expurgated narrow-sense BCH-code C(I) with length 156 | 54−1, defining interval I = [0,42], and minimum distance d ≥ |{−1,0,…,42}|+1 = 45 (BCH-bound) [i]
- linear OA(593, 156, F5, 40) (dual of [156, 63, 41]-code), using the narrow-sense BCH-code C(I) with length 156 | 54−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(51, 2, F5, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- linear OA(51, 9, F5, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-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.
Other Results with Identical Parameters
None.
Depending Results
None.