Information on Result #684069
Linear OA(5103, 130, F5, 64) (dual of [130, 27, 65]-code), using construction X applied to Ce(63) ⊂ Ce(61) based on
- linear OA(5102, 125, F5, 64) (dual of [125, 23, 65]-code), using an extension Ce(63) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,63], and designed minimum distance d ≥ |I|+1 = 64 [i]
- linear OA(598, 125, F5, 62) (dual of [125, 27, 63]-code), using an extension Ce(61) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,61], and designed minimum distance d ≥ |I|+1 = 62 [i]
- linear OA(51, 5, F5, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
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(5103, 130, F5, 63) (dual of [130, 27, 64]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(5103, 130, F5, 62) (dual of [130, 27, 63]-code) | [i] | ||
| 3 | Linear OA(5103, 130, F5, 61) (dual of [130, 27, 62]-code) | [i] | ||
| 4 | Linear OA(5103, 130, F5, 60) (dual of [130, 27, 61]-code) | [i] | ||
| 5 | Linear OA(5103, 130, F5, 59) (dual of [130, 27, 60]-code) | [i] | ||
| 6 | Linear OA(5103, 130, F5, 58) (dual of [130, 27, 59]-code) | [i] | ||
| 7 | Linear OA(5103, 130, F5, 57) (dual of [130, 27, 58]-code) | [i] | ||
| 8 | Linear OA(5103, 130, F5, 56) (dual of [130, 27, 57]-code) | [i] | ||
| 9 | Linear OA(5104, 131, F5, 64) (dual of [131, 27, 65]-code) | [i] | Code Embedding in Larger Space | |
| 10 | Linear OA(5102, 129, F5, 63) (dual of [129, 27, 64]-code) | [i] | Truncation | |
| 11 | Linear OA(5101, 128, F5, 62) (dual of [128, 27, 63]-code) | [i] | ||
| 12 | Linear OA(5100, 127, F5, 61) (dual of [127, 27, 62]-code) | [i] | ||
| 13 | Linear OA(596, 123, F5, 57) (dual of [123, 27, 58]-code) | [i] | ||
| 14 | Linear OA(595, 122, F5, 56) (dual of [122, 27, 57]-code) | [i] | ||
| 15 | Linear OA(594, 121, F5, 55) (dual of [121, 27, 56]-code) | [i] | ||
| 16 | Linear OA(593, 120, F5, 54) (dual of [120, 27, 55]-code) | [i] | ||
| 17 | Linear OA(592, 119, F5, 53) (dual of [119, 27, 54]-code) | [i] | ||
| 18 | Linear OA(591, 118, F5, 52) (dual of [118, 27, 53]-code) | [i] | ||
| 19 | Linear OA(590, 117, F5, 51) (dual of [117, 27, 52]-code) | [i] | ||
| 20 | Linear OA(589, 116, F5, 50) (dual of [116, 27, 51]-code) | [i] | ||
| 21 | Linear OA(588, 115, F5, 49) (dual of [115, 27, 50]-code) | [i] | ||
| 22 | Linear OA(587, 114, F5, 48) (dual of [114, 27, 49]-code) | [i] | ||
| 23 | Linear OA(586, 113, F5, 47) (dual of [113, 27, 48]-code) | [i] | ||
| 24 | Linear OA(585, 112, F5, 46) (dual of [112, 27, 47]-code) | [i] | ||
| 25 | Linear OA(584, 111, F5, 45) (dual of [111, 27, 46]-code) | [i] | ||
| 26 | Linear OA(583, 110, F5, 44) (dual of [110, 27, 45]-code) | [i] | ||
| 27 | Linear OA(582, 109, F5, 43) (dual of [109, 27, 44]-code) | [i] | ||
| 28 | Linear OA(5106, 135, F5, 60) (dual of [135, 29, 61]-code) | [i] | Varšamov–Edel Lengthening | |
| 29 | Linear OA(5109, 137, F5, 64) (dual of [137, 28, 65]-code) | [i] | Construction X with Varšamov Bound | |
| 30 | Linear OA(5113, 143, F5, 64) (dual of [143, 30, 65]-code) | [i] | ||
| 31 | Linear OA(5114, 145, F5, 64) (dual of [145, 31, 65]-code) | [i] | ||
| 32 | Linear OOA(5103, 65, F5, 2, 64) (dual of [(65, 2), 27, 65]-NRT-code) | [i] | OOA Folding | |
| 33 | Linear OOA(5103, 43, F5, 3, 64) (dual of [(43, 3), 26, 65]-NRT-code) | [i] | ||