Information on Result #701026
Linear OA(454, 83, F4, 24) (dual of [83, 29, 25]-code), using construction XX applied to C1 = C({1,2,3,5,7,9,10,11,13,14,15,21,22,23}), C2 = C([1,15]), C3 = C1 + C2 = C({1,2,3,5,7,9,10,11,13,14,15}), and C∩ = C1 ∩ C2 = C([1,23]) based on
- linear OA(440, 63, F4, 17) (dual of [63, 23, 18]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {1,2,3,5,7,9,10,11,13,14,15,21,22,23}, and minimum distance d ≥ |{7,8,…,23}|+1 = 18 (BCH-bound) [i]
- linear OA(436, 63, F4, 20) (dual of [63, 27, 21]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 21 [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(433, 63, F4, 14) (dual of [63, 30, 15]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {1,2,3,5,7,9,10,11,13,14,15}, and minimum distance d ≥ |{7,8,…,20}|+1 = 15 (BCH-bound) [i]
- linear OA(44, 11, F4, 3) (dual of [11, 7, 4]-code or 11-cap in PG(3,4)), using
- linear OA(47, 9, F4, 6) (dual of [9, 2, 7]-code), using
- 1 times truncation [i] based on linear OA(48, 10, F4, 7) (dual of [10, 2, 8]-code), using
- repeating each code word 2 times [i] based on linear OA(43, 5, F4, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,4) or 5-cap in PG(2,4)), using
- extended Reed–Solomon code RSe(2,4) [i]
- Simplex code S(2,4) [i]
- repeating each code word 2 times [i] based on linear OA(43, 5, F4, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,4) or 5-cap in PG(2,4)), using
- 1 times truncation [i] based on linear OA(48, 10, F4, 7) (dual of [10, 2, 8]-code), 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.