Information on Result #1299758
Linear OA(446, 74, F4, 23) (dual of [74, 28, 24]-code), using construction X with Varšamov bound based on
- linear OA(442, 69, F4, 23) (dual of [69, 27, 24]-code), using
- construction XX applied to C1 = C([0,62]), C2 = C([1,68]), C3 = C1 + C2 = C([1,62]), and C∩ = C1 ∩ C2 = C([0,68]) [i] based on
- linear OA(437, 63, F4, 21) (dual of [63, 26, 22]-code), using contraction [i] based on linear OA(4163, 189, F4, 65) (dual of [189, 26, 66]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,62], and minimum distance d ≥ |{−2,−1,…,62}|+1 = 66 (BCH-bound) [i]
- linear OA(440, 63, F4, 22) (dual of [63, 23, 23]-code), using contraction [i] based on linear OA(4166, 189, F4, 68) (dual of [189, 23, 69]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,68], and designed minimum distance d ≥ |I|+1 = 69 [i]
- linear OA(441, 63, F4, 23) (dual of [63, 22, 24]-code), using contraction [i] based on linear OA(4167, 189, F4, 71) (dual of [189, 22, 72]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,68], and minimum distance d ≥ |{−2,−1,…,68}|+1 = 72 (BCH-bound) [i]
- linear OA(436, 63, F4, 20) (dual of [63, 27, 21]-code), using contraction [i] based on linear OA(4162, 189, F4, 62) (dual of [189, 27, 63]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,62], and designed minimum distance d ≥ |I|+1 = 63 [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, 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
- construction XX applied to C1 = C([0,62]), C2 = C([1,68]), C3 = C1 + C2 = C([1,62]), and C∩ = C1 ∩ C2 = C([0,68]) [i] based on
- linear OA(442, 70, F4, 19) (dual of [70, 28, 20]-code), using Gilbert–Varšamov bound and bm = 442 > Vbs−1(k−1) = 7 537385 650690 554085 211032 [i]
- linear OA(43, 4, F4, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,4) or 4-cap in PG(2,4)), using
- dual of repetition code with length 4 [i]
- Reed–Solomon code RS(1,4) [i]
Mode: 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.