Information on Result #613106
Linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37
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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(4216, 65535, F4, 36) (dual of [65535, 65319, 37]-code) | [i] | Truncation | |
| 2 | Linear OA(4235, 65555, F4, 37) (dual of [65555, 65320, 38]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(4239, 65560, F4, 37) (dual of [65560, 65321, 38]-code) | [i] | ||
| 4 | Linear OA(4240, 65562, F4, 37) (dual of [65562, 65322, 38]-code) | [i] | ||
| 5 | Linear OA(4242, 65565, F4, 37) (dual of [65565, 65323, 38]-code) | [i] | ||
| 6 | Linear OA(4242, 65562, F4, 37) (dual of [65562, 65320, 38]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 7 | Linear OA(4225, 65544, F4, 38) (dual of [65544, 65319, 39]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 8 | Linear OA(4218, 65545, F4, 37) (dual of [65545, 65327, 38]-code) | [i] | ✔ | |
| 9 | Linear OA(4234, 65553, F4, 39) (dual of [65553, 65319, 40]-code) | [i] | ✔ | |
| 10 | Linear OA(4218, 65553, F4, 36) (dual of [65553, 65335, 37]-code) | [i] | ✔ | |
| 11 | Linear OA(4220, 65555, F4, 37) (dual of [65555, 65335, 38]-code) | [i] | ✔ | |
| 12 | Linear OA(4246, 65565, F4, 41) (dual of [65565, 65319, 42]-code) | [i] | ✔ | |
| 13 | Linear OA(4244, 65557, F4, 40) (dual of [65557, 65313, 41]-code) | [i] | ✔ | |
| 14 | Linear OA(4222, 65565, F4, 37) (dual of [65565, 65343, 38]-code) | [i] | ✔ | |
| 15 | Linear OA(4220, 65557, F4, 36) (dual of [65557, 65337, 37]-code) | [i] | ✔ | |
| 16 | Linear OA(4256, 65575, F4, 42) (dual of [65575, 65319, 43]-code) | [i] | ✔ | |
| 17 | Linear OA(4227, 65578, F4, 37) (dual of [65578, 65351, 38]-code) | [i] | ✔ | |
| 18 | Linear OA(4224, 65575, F4, 36) (dual of [65575, 65351, 37]-code) | [i] | ✔ | |
| 19 | Linear OA(4230, 65589, F4, 37) (dual of [65589, 65359, 38]-code) | [i] | ✔ | |
| 20 | Linear OA(4227, 65586, F4, 36) (dual of [65586, 65359, 37]-code) | [i] | ✔ | |
| 21 | Linear OA(4233, 65600, F4, 37) (dual of [65600, 65367, 38]-code) | [i] | ✔ | |
| 22 | Linear OA(4230, 65597, F4, 36) (dual of [65597, 65367, 37]-code) | [i] | ✔ | |
| 23 | Linear OA(4239, 65614, F4, 37) (dual of [65614, 65375, 38]-code) | [i] | ✔ | |
| 24 | Linear OA(4243, 65621, F4, 37) (dual of [65621, 65378, 38]-code) | [i] | ✔ | |
| 25 | Linear OA(4239, 65621, F4, 36) (dual of [65621, 65382, 37]-code) | [i] | ✔ | |
| 26 | Linear OA(4242, 65625, F4, 36) (dual of [65625, 65383, 37]-code) | [i] | ✔ | |
| 27 | Linear OA(4226, 65572, F4, 37) (dual of [65572, 65346, 38]-code) | [i] | ✔ | |
| 28 | Linear OA(4238, 65608, F4, 37) (dual of [65608, 65370, 38]-code) | [i] | ✔ | |
| 29 | Linear OA(4236, 65605, F4, 36) (dual of [65605, 65369, 37]-code) | [i] | ✔ | |
| 30 | Linear OA(4237, 65609, F4, 36) (dual of [65609, 65372, 37]-code) | [i] | ✔ | |
| 31 | Linear OA(4243, 65625, F4, 37) (dual of [65625, 65382, 38]-code) | [i] | ✔ | |
| 32 | Linear OA(4240, 65623, F4, 36) (dual of [65623, 65383, 37]-code) | [i] | ✔ | |
| 33 | Linear OA(4226, 65577, F4, 37) (dual of [65577, 65351, 38]-code) | [i] | ✔ | |
| 34 | Linear OA(4229, 65582, F4, 37) (dual of [65582, 65353, 38]-code) | [i] | ✔ | |
| 35 | Linear OA(4226, 65585, F4, 36) (dual of [65585, 65359, 37]-code) | [i] | ✔ | |
| 36 | Linear OA(4231, 65598, F4, 37) (dual of [65598, 65367, 38]-code) | [i] | ✔ | |
| 37 | Linear OA(4238, 65613, F4, 37) (dual of [65613, 65375, 38]-code) | [i] | ✔ | |
| 38 | Linear OA(4236, 65611, F4, 36) (dual of [65611, 65375, 37]-code) | [i] | ✔ | |
| 39 | Linear OA(4240, 65621, F4, 37) (dual of [65621, 65381, 38]-code) | [i] | ✔ | |
| 40 | Linear OA(4241, 65624, F4, 37) (dual of [65624, 65383, 38]-code) | [i] | ✔ | |
| 41 | Linear OA(4238, 65621, F4, 36) (dual of [65621, 65383, 37]-code) | [i] | ✔ | |
| 42 | Linear OA(4255, 65567, F4, 42) (dual of [65567, 65312, 43]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 43 | Linear OA(4245, 65557, F4, 41) (dual of [65557, 65312, 42]-code) | [i] | ✔ | |
| 44 | Linear OA(4243, 65555, F4, 40) (dual of [65555, 65312, 41]-code) | [i] | ✔ | |
| 45 | Linear OA(4249, 65570, F4, 41) (dual of [65570, 65321, 42]-code) | [i] | ✔ | |
| 46 | Linear OA(4248, 65568, F4, 41) (dual of [65568, 65320, 42]-code) | [i] | ✔ | |
| 47 | Linear OA(4237, 65558, F4, 39) (dual of [65558, 65321, 40]-code) | [i] | ✔ | |
| 48 | Linear OA(4236, 65556, F4, 39) (dual of [65556, 65320, 40]-code) | [i] | ✔ | |
| 49 | Linear OA(4227, 65547, F4, 38) (dual of [65547, 65320, 39]-code) | [i] | ✔ | |
| 50 | Linear OA(4219, 65547, F4, 37) (dual of [65547, 65328, 38]-code) | [i] | ✔ | |
| 51 | Linear OA(4221, 65557, F4, 37) (dual of [65557, 65336, 38]-code) | [i] | ✔ | |
| 52 | Linear OA(4219, 65555, F4, 36) (dual of [65555, 65336, 37]-code) | [i] | ✔ | |
| 53 | Linear OA(4225, 65570, F4, 37) (dual of [65570, 65345, 38]-code) | [i] | ✔ | |
| 54 | Linear OA(4224, 65568, F4, 37) (dual of [65568, 65344, 38]-code) | [i] | ✔ | |
| 55 | Linear OOA(4217, 32768, F4, 2, 37) (dual of [(32768, 2), 65319, 38]-NRT-code) | [i] | OOA Folding | |
| 56 | Linear OOA(4217, 21845, F4, 3, 37) (dual of [(21845, 3), 65318, 38]-NRT-code) | [i] | ||
| 57 | Linear OOA(4217, 3640, F4, 37, 37) (dual of [(3640, 37), 134463, 38]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |