Information on Result #612866
Linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21
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(4120, 65535, F4, 20) (dual of [65535, 65415, 21]-code) | [i] | Truncation | |
| 2 | Linear OA(4131, 65547, F4, 21) (dual of [65547, 65416, 22]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(4133, 65552, F4, 21) (dual of [65552, 65419, 22]-code) | [i] | ||
| 4 | Linear OA(4135, 65565, F4, 21) (dual of [65565, 65430, 22]-code) | [i] | ||
| 5 | Linear OA(4129, 65544, F4, 22) (dual of [65544, 65415, 23]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 6 | Linear OA(4122, 65545, F4, 21) (dual of [65545, 65423, 22]-code) | [i] | ✔ | |
| 7 | Linear OA(4138, 65553, F4, 23) (dual of [65553, 65415, 24]-code) | [i] | ✔ | |
| 8 | Linear OA(4122, 65553, F4, 20) (dual of [65553, 65431, 21]-code) | [i] | ✔ | |
| 9 | Linear OA(4124, 65555, F4, 21) (dual of [65555, 65431, 22]-code) | [i] | ✔ | |
| 10 | Linear OA(4150, 65565, F4, 25) (dual of [65565, 65415, 26]-code) | [i] | ✔ | |
| 11 | Linear OA(4148, 65557, F4, 24) (dual of [65557, 65409, 25]-code) | [i] | ✔ | |
| 12 | Linear OA(4126, 65565, F4, 21) (dual of [65565, 65439, 22]-code) | [i] | ✔ | |
| 13 | Linear OA(4124, 65557, F4, 20) (dual of [65557, 65433, 21]-code) | [i] | ✔ | |
| 14 | Linear OA(4160, 65575, F4, 26) (dual of [65575, 65415, 27]-code) | [i] | ✔ | |
| 15 | Linear OA(4131, 65578, F4, 21) (dual of [65578, 65447, 22]-code) | [i] | ✔ | |
| 16 | Linear OA(4128, 65575, F4, 20) (dual of [65575, 65447, 21]-code) | [i] | ✔ | |
| 17 | Linear OA(4171, 65586, F4, 27) (dual of [65586, 65415, 28]-code) | [i] | ✔ | |
| 18 | Linear OA(4134, 65589, F4, 21) (dual of [65589, 65455, 22]-code) | [i] | ✔ | |
| 19 | Linear OA(4131, 65586, F4, 20) (dual of [65586, 65455, 21]-code) | [i] | ✔ | |
| 20 | Linear OA(4185, 65600, F4, 29) (dual of [65600, 65415, 30]-code) | [i] | ✔ | |
| 21 | Linear OA(4182, 65597, F4, 28) (dual of [65597, 65415, 29]-code) | [i] | ✔ | |
| 22 | Linear OA(4134, 65597, F4, 20) (dual of [65597, 65463, 21]-code) | [i] | ✔ | |
| 23 | Linear OA(4198, 65613, F4, 30) (dual of [65613, 65415, 31]-code) | [i] | ✔ | |
| 24 | Linear OA(4207, 65621, F4, 31) (dual of [65621, 65414, 32]-code) | [i] | ✔ | |
| 25 | Linear OA(4130, 65572, F4, 21) (dual of [65572, 65442, 22]-code) | [i] | ✔ | |
| 26 | Linear OA(4196, 65605, F4, 30) (dual of [65605, 65409, 31]-code) | [i] | ✔ | |
| 27 | Linear OA(4197, 65609, F4, 30) (dual of [65609, 65412, 31]-code) | [i] | ✔ | |
| 28 | Linear OA(4130, 65577, F4, 21) (dual of [65577, 65447, 22]-code) | [i] | ✔ | |
| 29 | Linear OA(4170, 65585, F4, 27) (dual of [65585, 65415, 28]-code) | [i] | ✔ | |
| 30 | Linear OA(4133, 65582, F4, 21) (dual of [65582, 65449, 22]-code) | [i] | ✔ | |
| 31 | Linear OA(4130, 65585, F4, 20) (dual of [65585, 65455, 21]-code) | [i] | ✔ | |
| 32 | Linear OA(4183, 65598, F4, 29) (dual of [65598, 65415, 30]-code) | [i] | ✔ | |
| 33 | Linear OA(4135, 65598, F4, 21) (dual of [65598, 65463, 22]-code) | [i] | ✔ | |
| 34 | Linear OA(4195, 65604, F4, 30) (dual of [65604, 65409, 31]-code) | [i] | ✔ | |
| 35 | Linear OA(4196, 65611, F4, 30) (dual of [65611, 65415, 31]-code) | [i] | ✔ | |
| 36 | Linear OA(4206, 65621, F4, 31) (dual of [65621, 65415, 32]-code) | [i] | ✔ | |
| 37 | Linear OA(4159, 65567, F4, 26) (dual of [65567, 65408, 27]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 38 | Linear OA(4149, 65557, F4, 25) (dual of [65557, 65408, 26]-code) | [i] | ✔ | |
| 39 | Linear OA(4147, 65555, F4, 24) (dual of [65555, 65408, 25]-code) | [i] | ✔ | |
| 40 | Linear OA(4153, 65570, F4, 25) (dual of [65570, 65417, 26]-code) | [i] | ✔ | |
| 41 | Linear OA(4152, 65568, F4, 25) (dual of [65568, 65416, 26]-code) | [i] | ✔ | |
| 42 | Linear OA(4141, 65558, F4, 23) (dual of [65558, 65417, 24]-code) | [i] | ✔ | |
| 43 | Linear OA(4140, 65556, F4, 23) (dual of [65556, 65416, 24]-code) | [i] | ✔ | |
| 44 | Linear OA(4131, 65547, F4, 22) (dual of [65547, 65416, 23]-code) | [i] | ✔ | |
| 45 | Linear OA(4123, 65547, F4, 21) (dual of [65547, 65424, 22]-code) | [i] | ✔ | |
| 46 | Linear OA(4125, 65557, F4, 21) (dual of [65557, 65432, 22]-code) | [i] | ✔ | |
| 47 | Linear OA(4123, 65555, F4, 20) (dual of [65555, 65432, 21]-code) | [i] | ✔ | |
| 48 | Linear OA(4129, 65570, F4, 21) (dual of [65570, 65441, 22]-code) | [i] | ✔ | |
| 49 | Linear OA(4128, 65568, F4, 21) (dual of [65568, 65440, 22]-code) | [i] | ✔ | |
| 50 | Linear OA(4146, 65562, F4, 23) (dual of [65562, 65416, 24]-code) | [i] | ✔ | Construction X4 with Extended Narrow-Sense BCH Codes |
| 51 | Linear OOA(4121, 32768, F4, 2, 21) (dual of [(32768, 2), 65415, 22]-NRT-code) | [i] | OOA Folding | |
| 52 | Linear OOA(4121, 21845, F4, 3, 21) (dual of [(21845, 3), 65414, 22]-NRT-code) | [i] | ||
| 53 | Linear OOA(4121, 6553, F4, 21, 21) (dual of [(6553, 21), 137492, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |