Information on Result #737724
Linear OA(5111, 138, F5, 68) (dual of [138, 27, 69]-code), using construction XX applied to Ce(67) ⊂ Ce(62) ⊂ Ce(61) based on
- linear OA(5105, 125, F5, 68) (dual of [125, 20, 69]-code), using an extension Ce(67) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,67], and designed minimum distance d ≥ |I|+1 = 68 [i]
- linear OA(599, 125, F5, 63) (dual of [125, 26, 64]-code), using an extension Ce(62) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,62], and designed minimum distance d ≥ |I|+1 = 63 [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(55, 12, F5, 4) (dual of [12, 7, 5]-code), using
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
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(5111, 138, F5, 67) (dual of [138, 27, 68]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(5111, 138, F5, 66) (dual of [138, 27, 67]-code) | [i] | ||
| 3 | Linear OA(5111, 138, F5, 65) (dual of [138, 27, 66]-code) | [i] | ||
| 4 | Linear OA(5111, 138, F5, 64) (dual of [138, 27, 65]-code) | [i] | ||
| 5 | Linear OA(5111, 138, F5, 63) (dual of [138, 27, 64]-code) | [i] | ||
| 6 | Linear OA(5113, 140, F5, 68) (dual of [140, 27, 69]-code) | [i] | Code Embedding in Larger Space | |
| 7 | Linear OA(5114, 141, F5, 68) (dual of [141, 27, 69]-code) | [i] | ||
| 8 | Linear OA(5108, 135, F5, 65) (dual of [135, 27, 66]-code) | [i] | Truncation | |
| 9 | Linear OA(5107, 134, F5, 64) (dual of [134, 27, 65]-code) | [i] | ||
| 10 | Linear OA(5105, 132, F5, 62) (dual of [132, 27, 63]-code) | [i] | ||
| 11 | Linear OA(5104, 131, F5, 61) (dual of [131, 27, 62]-code) | [i] | ||
| 12 | Linear OA(5102, 129, F5, 59) (dual of [129, 27, 60]-code) | [i] | ||
| 13 | Linear OA(5101, 128, F5, 58) (dual of [128, 27, 59]-code) | [i] | ||
| 14 | Linear OA(5100, 127, F5, 57) (dual of [127, 27, 58]-code) | [i] | ||
| 15 | Linear OA(596, 123, F5, 53) (dual of [123, 27, 54]-code) | [i] | ||
| 16 | Linear OA(595, 122, F5, 52) (dual of [122, 27, 53]-code) | [i] | ||
| 17 | Linear OA(594, 121, F5, 51) (dual of [121, 27, 52]-code) | [i] | ||
| 18 | Linear OA(593, 120, F5, 50) (dual of [120, 27, 51]-code) | [i] | ||
| 19 | Linear OA(592, 119, F5, 49) (dual of [119, 27, 50]-code) | [i] | ||
| 20 | Linear OA(591, 118, F5, 48) (dual of [118, 27, 49]-code) | [i] | ||
| 21 | Linear OA(5119, 149, F5, 68) (dual of [149, 30, 69]-code) | [i] | Varšamov–Edel Lengthening | |
| 22 | Linear OA(5120, 151, F5, 68) (dual of [151, 31, 69]-code) | [i] | ||
| 23 | Linear OA(5116, 144, F5, 68) (dual of [144, 28, 69]-code) | [i] | Construction X with Varšamov Bound | |
| 24 | Linear OOA(5111, 69, F5, 2, 68) (dual of [(69, 2), 27, 69]-NRT-code) | [i] | OOA Folding | |
| 25 | Linear OOA(5111, 46, F5, 3, 68) (dual of [(46, 3), 27, 69]-NRT-code) | [i] | ||