Information on Result #700961
Linear OA(49, 17, F4, 7) (dual of [17, 8, 8]-code), using the cyclic code C(A) with length 17 | 44−1, defining set A = {0,1,3}, and minimum distance d ≥ |{1,5}| + |{−6,−5,…,0}∖{−3}| = 8 (general Roos-bound)
Mode: Constructive and linear.
This result is hidden, because other results with identical parameters exist.
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
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(424, 32, F4, 15) (dual of [32, 8, 16]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(425, 34, F4, 15) (dual of [34, 9, 16]-code) | [i] | ||
| 3 | Linear OA(476, 4113, F4, 15) (dual of [4113, 4037, 16]-code) | [i] | ||
| 4 | Linear OA(487, 16401, F4, 15) (dual of [16401, 16314, 16]-code) | [i] | ||
| 5 | Linear OA(498, 65553, F4, 15) (dual of [65553, 65455, 16]-code) | [i] | ||
| 6 | Linear OA(4109, 262161, F4, 15) (dual of [262161, 262052, 16]-code) | [i] | ||
| 7 | Linear OA(4120, 1048593, F4, 15) (dual of [1048593, 1048473, 16]-code) | [i] | ||
| 8 | Linear OA(4131, 4194321, F4, 15) (dual of [4194321, 4194190, 16]-code) | [i] | ||
| 9 | Linear OA(460, 1041, F4, 14) (dual of [1041, 981, 15]-code) | [i] | ||
| 10 | Linear OA(480, 16401, F4, 14) (dual of [16401, 16321, 15]-code) | [i] | ||
| 11 | Linear OA(490, 65553, F4, 14) (dual of [65553, 65463, 15]-code) | [i] | ||
| 12 | Linear OA(4100, 262161, F4, 14) (dual of [262161, 262061, 15]-code) | [i] | ||
| 13 | Linear OA(4110, 1048593, F4, 14) (dual of [1048593, 1048483, 15]-code) | [i] | ||
| 14 | Linear OA(4120, 4194321, F4, 14) (dual of [4194321, 4194201, 15]-code) | [i] | ||
| 15 | Linear OA(413, 34, F4, 7) (dual of [34, 21, 8]-code) | [i] | ||
| 16 | Linear OA(417, 68, F4, 7) (dual of [68, 51, 8]-code) | [i] | Generalized (u, u+v)-Construction | |
| 17 | Linear OA(498, 103, F4, 71) (dual of [103, 5, 72]-code) | [i] | Juxtaposition | |
| 18 | Linear OA(494, 98, F4, 71) (dual of [98, 4, 72]-code) | [i] | ||
| 19 | Linear OA(235, 51, F2, 15) (dual of [51, 16, 16]-code) | [i] | Concatenation of Two Codes | |
| 20 | Linear OA(234, 48, F2, 15) (dual of [48, 14, 16]-code) | [i] | ||
| 21 | Linear OA(233, 45, F2, 15) (dual of [45, 12, 16]-code) | [i] | ||
| 22 | Linear OOA(286, 51, F2, 2, 39) (dual of [(51, 2), 16, 40]-NRT-code) | [i] | Concatenation of Two NRT-Codes | |
| 23 | Linear OOA(282, 48, F2, 2, 39) (dual of [(48, 2), 14, 40]-NRT-code) | [i] | ||
| 24 | Linear OOA(278, 45, F2, 2, 39) (dual of [(45, 2), 12, 40]-NRT-code) | [i] | ||
| 25 | Linear OOA(274, 42, F2, 2, 39) (dual of [(42, 2), 10, 40]-NRT-code) | [i] | ||
| 26 | Linear OOA(270, 39, F2, 2, 39) (dual of [(39, 2), 8, 40]-NRT-code) | [i] | ||
| 27 | Linear OOA(266, 36, F2, 2, 39) (dual of [(36, 2), 6, 40]-NRT-code) | [i] | ||
| 28 | Linear OA(415, 39, F4, 7) (dual of [39, 24, 8]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 29 | Linear OA(4258, 274, F4, 179) (dual of [274, 16, 180]-code) | [i] | Construction X with Cyclic Codes | |
| 30 | Linear OA(429, 36, F4, 18) (dual of [36, 7, 19]-code) | [i] | ||
| 31 | Linear OA(49, 18, F4, 7) (dual of [18, 9, 8]-code) | [i] | ✔ | |
| 32 | Linear OA(451, 84, F4, 23) (dual of [84, 33, 24]-code) | [i] | Construction XX with Cyclic Codes | |
| 33 | Linear OA(455, 87, F4, 24) (dual of [87, 32, 25]-code) | [i] | ||
| 34 | Linear OA(450, 82, F4, 23) (dual of [82, 32, 24]-code) | [i] | ||
| 35 | Linear OA(454, 86, F4, 24) (dual of [86, 32, 25]-code) | [i] | ||
| 36 | Linear OA(457, 90, F4, 25) (dual of [90, 33, 26]-code) | [i] | ||
| 37 | Linear OA(456, 88, F4, 25) (dual of [88, 32, 26]-code) | [i] | ||
| 38 | Linear OA(454, 83, F4, 25) (dual of [83, 29, 26]-code) | [i] | ||
| 39 | Linear OA(4209, 273, F4, 102) (dual of [273, 64, 103]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 40 | Linear OA(4202, 211, F4, 139) (dual of [211, 9, 140]-code) | [i] | ||
| 41 | Linear OA(4202, 212, F4, 138) (dual of [212, 10, 139]-code) | [i] | ||
| 42 | Linear OA(450, 80, F4, 23) (dual of [80, 30, 24]-code) | [i] | ||
| 43 | Linear OA(447, 80, F4, 22) (dual of [80, 33, 23]-code) | [i] | ||
| 44 | Linear OA(446, 81, F4, 21) (dual of [81, 35, 22]-code) | [i] | ||
| 45 | Linear OA(4203, 213, F4, 139) (dual of [213, 10, 140]-code) | [i] | Construction XX with a Chain of Extended Narrow-Sense BCH Codes | |
| 46 | Linear OA(451, 82, F4, 23) (dual of [82, 31, 24]-code) | [i] | ||
| 47 | Linear OA(448, 82, F4, 22) (dual of [82, 34, 23]-code) | [i] | ||
| 48 | Linear OA(492, 98, F4, 67) (dual of [98, 6, 68]-code) | [i] | Construction X with De Boer–Brouwer Codes | |