Information on Result #700995
Linear OA(425, 69, F4, 11) (dual of [69, 44, 12]-code), using construction XX applied to C1 = C({0,1,2,3,5,6,7,47}), C2 = C([0,9]), C3 = C1 + C2 = C([0,7]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,9,47}) based on
- linear OA(422, 63, F4, 10) (dual of [63, 41, 11]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,47}, and minimum distance d ≥ |{−1,0,…,8}|+1 = 11 (BCH-bound) [i]
- linear OA(422, 63, F4, 10) (dual of [63, 41, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(425, 63, F4, 11) (dual of [63, 38, 12]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,47}, and minimum distance d ≥ |{−1,0,…,9}|+1 = 12 (BCH-bound) [i]
- linear OA(419, 63, F4, 9) (dual of [63, 44, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(40, 3, F4, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(40, 3, F4, 0) (dual of [3, 3, 1]-code) (see above)
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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(4156, 1092, F4, 35) (dual of [1092, 936, 36]-code) | [i] | Construction X with Cyclic Codes | |
| 2 | Linear OA(4160, 1092, F4, 36) (dual of [1092, 932, 37]-code) | [i] | ||
| 3 | Linear OA(4161, 1092, F4, 37) (dual of [1092, 931, 38]-code) | [i] | ||
| 4 | Linear OA(4166, 1092, F4, 38) (dual of [1092, 926, 39]-code) | [i] | ||
| 5 | Linear OA(4171, 1092, F4, 39) (dual of [1092, 921, 40]-code) | [i] | ||
| 6 | Linear OA(4175, 1092, F4, 40) (dual of [1092, 917, 41]-code) | [i] | ||
| 7 | Linear OA(4176, 1092, F4, 41) (dual of [1092, 916, 42]-code) | [i] | ||
| 8 | Linear OA(4181, 1092, F4, 42) (dual of [1092, 911, 43]-code) | [i] | ||
| 9 | Linear OA(4186, 1092, F4, 43) (dual of [1092, 906, 44]-code) | [i] | ||
| 10 | Linear OA(4190, 1092, F4, 44) (dual of [1092, 902, 45]-code) | [i] | ||
| 11 | Linear OA(4191, 1092, F4, 45) (dual of [1092, 901, 46]-code) | [i] | ||
| 12 | Linear OA(4196, 1092, F4, 46) (dual of [1092, 896, 47]-code) | [i] | ||
| 13 | Linear OA(4201, 1092, F4, 47) (dual of [1092, 891, 48]-code) | [i] | ||
| 14 | Linear OA(4205, 1092, F4, 48) (dual of [1092, 887, 49]-code) | [i] | ||
| 15 | Linear OA(4206, 1092, F4, 49) (dual of [1092, 886, 50]-code) | [i] | ||
| 16 | Linear OA(4211, 1092, F4, 50) (dual of [1092, 881, 51]-code) | [i] | ||
| 17 | Linear OA(4216, 1092, F4, 51) (dual of [1092, 876, 52]-code) | [i] | ||
| 18 | Linear OA(4220, 1092, F4, 52) (dual of [1092, 872, 53]-code) | [i] | ||
| 19 | Linear OA(4221, 1092, F4, 53) (dual of [1092, 871, 54]-code) | [i] | ||
| 20 | Linear OA(4226, 1092, F4, 54) (dual of [1092, 866, 55]-code) | [i] | ||
| 21 | Linear OA(4231, 1092, F4, 55) (dual of [1092, 861, 56]-code) | [i] | ||
| 22 | Linear OA(4235, 1092, F4, 56) (dual of [1092, 857, 57]-code) | [i] | ||
| 23 | Linear OA(4236, 1092, F4, 57) (dual of [1092, 856, 58]-code) | [i] | ||
| 24 | Linear OA(4241, 1092, F4, 58) (dual of [1092, 851, 59]-code) | [i] | ||
| 25 | Linear OA(4246, 1092, F4, 59) (dual of [1092, 846, 60]-code) | [i] | ||
| 26 | Linear OA(4250, 1092, F4, 60) (dual of [1092, 842, 61]-code) | [i] | ||
| 27 | Linear OA(4251, 1092, F4, 61) (dual of [1092, 841, 62]-code) | [i] | ||
| 28 | Linear OA(4256, 1092, F4, 62) (dual of [1092, 836, 63]-code) | [i] | ||
| 29 | Linear OA(4242, 4166, F4, 49) (dual of [4166, 3924, 50]-code) | [i] | ||
| 30 | Linear OA(4206, 4166, F4, 41) (dual of [4166, 3960, 42]-code) | [i] | ||
| 31 | Linear OA(4256, 1093, F4, 62) (dual of [1093, 837, 63]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 32 | Linear OA(4251, 1093, F4, 61) (dual of [1093, 842, 62]-code) | [i] | ||
| 33 | Linear OA(4246, 1093, F4, 59) (dual of [1093, 847, 60]-code) | [i] | ||
| 34 | Linear OA(4241, 1093, F4, 58) (dual of [1093, 852, 59]-code) | [i] | ||
| 35 | Linear OA(4236, 1093, F4, 57) (dual of [1093, 857, 58]-code) | [i] | ||
| 36 | Linear OA(4231, 1093, F4, 55) (dual of [1093, 862, 56]-code) | [i] | ||
| 37 | Linear OA(4226, 1093, F4, 54) (dual of [1093, 867, 55]-code) | [i] | ||
| 38 | Linear OA(4221, 1093, F4, 53) (dual of [1093, 872, 54]-code) | [i] | ||
| 39 | Linear OA(4216, 1093, F4, 51) (dual of [1093, 877, 52]-code) | [i] | ||
| 40 | Linear OA(4211, 1093, F4, 50) (dual of [1093, 882, 51]-code) | [i] | ||
| 41 | Linear OA(4206, 1093, F4, 49) (dual of [1093, 887, 50]-code) | [i] | ||
| 42 | Linear OA(4201, 1093, F4, 47) (dual of [1093, 892, 48]-code) | [i] | ||
| 43 | Linear OA(4196, 1093, F4, 46) (dual of [1093, 897, 47]-code) | [i] | ||
| 44 | Linear OA(4191, 1093, F4, 45) (dual of [1093, 902, 46]-code) | [i] | ||
| 45 | Linear OA(4186, 1093, F4, 43) (dual of [1093, 907, 44]-code) | [i] | ||
| 46 | Linear OA(4181, 1093, F4, 42) (dual of [1093, 912, 43]-code) | [i] | ||
| 47 | Linear OA(4176, 1093, F4, 41) (dual of [1093, 917, 42]-code) | [i] | ||
| 48 | Linear OA(4171, 1093, F4, 39) (dual of [1093, 922, 40]-code) | [i] | ||
| 49 | Linear OA(4166, 1093, F4, 38) (dual of [1093, 927, 39]-code) | [i] | ||
| 50 | Linear OA(4161, 1093, F4, 37) (dual of [1093, 932, 38]-code) | [i] | ||
| 51 | Linear OA(4156, 1093, F4, 35) (dual of [1093, 937, 36]-code) | [i] | ||
| 52 | Linear OOA(425, 34, F4, 2, 11) (dual of [(34, 2), 43, 12]-NRT-code) | [i] | OOA Folding | |