Information on Result #609934
Linear OA(413, 17, F4, 11) (dual of [17, 4, 12]-code), using projective code from ovoid in PG(3, 4)
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(413, 17, F4, 10) (dual of [17, 4, 11]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(414, 18, F4, 11) (dual of [18, 4, 12]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(412, 16, F4, 10) (dual of [16, 4, 11]-code) | [i] | Truncation | |
| 4 | Linear OA(411, 15, F4, 9) (dual of [15, 4, 10]-code) | [i] | ||
| 5 | Linear OA(410, 14, F4, 8) (dual of [14, 4, 9]-code) | [i] | ||
| 6 | Linear OA(430, 34, F4, 23) (dual of [34, 4, 24]-code) | [i] | Repeating Each Code Word | |
| 7 | Linear OA(4116, 4113, F4, 23) (dual of [4113, 3997, 24]-code) | [i] | (u, u+v)-Construction | |
| 8 | Linear OA(4133, 16401, F4, 23) (dual of [16401, 16268, 24]-code) | [i] | ||
| 9 | Linear OA(4150, 65553, F4, 23) (dual of [65553, 65403, 24]-code) | [i] | ||
| 10 | Linear OA(4167, 262161, F4, 23) (dual of [262161, 261994, 24]-code) | [i] | ||
| 11 | Linear OA(4184, 1048593, F4, 23) (dual of [1048593, 1048409, 24]-code) | [i] | ||
| 12 | Linear OA(4201, 4194321, F4, 23) (dual of [4194321, 4194120, 24]-code) | [i] | ||
| 13 | Linear OA(451, 82, F4, 22) (dual of [82, 31, 23]-code) | [i] | ||
| 14 | Linear OA(4110, 4113, F4, 22) (dual of [4113, 4003, 23]-code) | [i] | ||
| 15 | Linear OA(4126, 16401, F4, 22) (dual of [16401, 16275, 23]-code) | [i] | ||
| 16 | Linear OA(4142, 65553, F4, 22) (dual of [65553, 65411, 23]-code) | [i] | ||
| 17 | Linear OA(4158, 262161, F4, 22) (dual of [262161, 262003, 23]-code) | [i] | ||
| 18 | Linear OA(4174, 1048593, F4, 22) (dual of [1048593, 1048419, 23]-code) | [i] | ||
| 19 | Linear OA(4190, 4194321, F4, 22) (dual of [4194321, 4194131, 23]-code) | [i] | ||
| 20 | Linear OA(417, 21, F4, 12) (dual of [21, 4, 13]-code) | [i] | Juxtaposition | |
| 21 | Linear OA(418, 22, F4, 13) (dual of [22, 4, 14]-code) | [i] | ||
| 22 | Linear OA(422, 26, F4, 16) (dual of [26, 4, 17]-code) | [i] | ||
| 23 | Linear OA(423, 27, F4, 17) (dual of [27, 4, 18]-code) | [i] | ||
| 24 | Linear OA(488, 92, F4, 67) (dual of [92, 4, 68]-code) | [i] | ||
| 25 | Linear OA(493, 97, F4, 71) (dual of [97, 4, 72]-code) | [i] | ||
| 26 | Linear OA(498, 102, F4, 75) (dual of [102, 4, 76]-code) | [i] | ||
| 27 | Linear OA(243, 51, F2, 23) (dual of [51, 8, 24]-code) | [i] | Concatenation of Two Codes | |
| 28 | Linear OOA(260, 34, F2, 2, 35) (dual of [(34, 2), 8, 36]-NRT-code) | [i] | Concatenation of Two NRT-Codes | |
| 29 | Linear OOA(258, 32, F2, 2, 35) (dual of [(32, 2), 6, 36]-NRT-code) | [i] | ||
| 30 | Linear OOA(294, 51, F2, 2, 59) (dual of [(51, 2), 8, 60]-NRT-code) | [i] | ||
| 31 | Linear OOA(290, 48, F2, 2, 59) (dual of [(48, 2), 6, 60]-NRT-code) | [i] | ||
| 32 | Linear OOA(286, 45, F2, 2, 59) (dual of [(45, 2), 4, 60]-NRT-code) | [i] | ||
| 33 | Linear OOA(294, 34, F2, 3, 59) (dual of [(34, 3), 8, 60]-NRT-code) | [i] | ||
| 34 | Linear OOA(2145, 51, F2, 3, 95) (dual of [(51, 3), 8, 96]-NRT-code) | [i] | ||
| 35 | Linear OOA(2138, 48, F2, 3, 95) (dual of [(48, 3), 6, 96]-NRT-code) | [i] | ||
| 36 | Linear OA(424, 49, F4, 11) (dual of [49, 25, 12]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 37 | Linear OA(4201, 208, F4, 143) (dual of [208, 7, 144]-code) | [i] | Construction XX with Cyclic Codes | |
| 38 | Linear OA(4202, 209, F4, 143) (dual of [209, 7, 144]-code) | [i] | Construction XX with a Chain of Cyclic Codes | |
| 39 | Linear OA(4199, 206, F4, 141) (dual of [206, 7, 142]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 40 | Linear OA(4199, 207, F4, 138) (dual of [207, 8, 139]-code) | [i] | ||
| 41 | Linear OA(4202, 210, F4, 141) (dual of [210, 8, 142]-code) | [i] | Construction XX with a Chain of Extended Narrow-Sense BCH Codes | |
| 42 | Linear OA(492, 102, F4, 59) (dual of [102, 10, 60]-code) | [i] | Construction X with De Boer–Brouwer Codes | |
| 43 | Linear OA(4110, 120, F4, 67) (dual of [120, 10, 68]-code) | [i] | Construction XX with a Chain of De Boer–Brouwer Codes | |
| 44 | Linear OA(4108, 118, F4, 66) (dual of [118, 10, 67]-code) | [i] | ||
| 45 | Linear OA(4104, 114, F4, 63) (dual of [114, 10, 64]-code) | [i] | ||
| 46 | Linear OA(4101, 111, F4, 61) (dual of [111, 10, 62]-code) | [i] | ||
| 47 | Linear OA(4109, 118, F4, 67) (dual of [118, 9, 68]-code) | [i] | ||
| 48 | Linear OA(4107, 116, F4, 66) (dual of [116, 9, 67]-code) | [i] | ||
| 49 | Linear OA(4103, 112, F4, 63) (dual of [112, 9, 64]-code) | [i] | ||
| 50 | Linear OA(4100, 109, F4, 61) (dual of [109, 9, 62]-code) | [i] | ||
| 51 | Linear OA(4108, 116, F4, 67) (dual of [116, 8, 68]-code) | [i] | ||
| 52 | Linear OA(4106, 114, F4, 66) (dual of [114, 8, 67]-code) | [i] | ||
| 53 | Linear OA(4104, 112, F4, 65) (dual of [112, 8, 66]-code) | [i] | ||
| 54 | Linear OA(499, 107, F4, 61) (dual of [107, 8, 62]-code) | [i] | ||
| 55 | Linear OA(419, 23, F4, 15) (dual of [23, 4, 16]-code) | [i] | ✔ | Construction X with Ovoid |
| 56 | Linear OOA(413, 8, F4, 2, 11) (dual of [(8, 2), 3, 12]-NRT-code) | [i] | OOA Folding | |