Information on Result #681999
Linear OA(451, 71, F4, 28) (dual of [71, 20, 29]-code), using construction XX applied to C1 = C([0,77]), C2 = C([1,89]), C3 = C1 + C2 = C([1,77]), and C∩ = C1 ∩ C2 = C([0,89]) based on
- linear OA(444, 63, F4, 26) (dual of [63, 19, 27]-code), using contraction [i] based on linear OA(4170, 189, F4, 80) (dual of [189, 19, 81]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,77], and minimum distance d ≥ |{−2,−1,…,77}|+1 = 81 (BCH-bound) [i]
- linear OA(449, 63, F4, 29) (dual of [63, 14, 30]-code), using contraction [i] based on linear OA(4175, 189, F4, 89) (dual of [189, 14, 90]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,89], and designed minimum distance d ≥ |I|+1 = 90 [i]
- linear OA(450, 63, F4, 30) (dual of [63, 13, 31]-code), using contraction [i] based on linear OA(4176, 189, F4, 92) (dual of [189, 13, 93]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,89], and minimum distance d ≥ |{−2,−1,…,89}|+1 = 93 (BCH-bound) [i]
- linear OA(443, 63, F4, 25) (dual of [63, 20, 26]-code), using contraction [i] based on linear OA(4169, 189, F4, 77) (dual of [189, 20, 78]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,77], and designed minimum distance d ≥ |I|+1 = 78 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- linear OA(41, 7, F4, 1) (dual of [7, 6, 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
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.