Information on Result #684234
Linear OA(5116, 143, F5, 69) (dual of [143, 27, 70]-code), using construction XX applied to Ce(68) ⊂ Ce(62) ⊂ Ce(61) based on
- linear OA(5108, 125, F5, 69) (dual of [125, 17, 70]-code), using an extension Ce(68) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,68], and designed minimum distance d ≥ |I|+1 = 69 [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(57, 17, F5, 5) (dual of [17, 10, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(57, 21, F5, 5) (dual of [21, 14, 6]-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(5116, 143, F5, 68) (dual of [143, 27, 69]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(5116, 143, F5, 67) (dual of [143, 27, 68]-code) | [i] | ||
| 3 | Linear OA(5116, 143, F5, 66) (dual of [143, 27, 67]-code) | [i] | ||
| 4 | Linear OA(5116, 143, F5, 65) (dual of [143, 27, 66]-code) | [i] | ||
| 5 | Linear OA(5115, 142, F5, 68) (dual of [142, 27, 69]-code) | [i] | Truncation | |
| 6 | Linear OA(5114, 141, F5, 67) (dual of [141, 27, 68]-code) | [i] | ||
| 7 | Linear OA(5113, 140, F5, 66) (dual of [140, 27, 67]-code) | [i] | ||
| 8 | Linear OA(5108, 135, F5, 61) (dual of [135, 27, 62]-code) | [i] | ||
| 9 | Linear OA(5107, 134, F5, 60) (dual of [134, 27, 61]-code) | [i] | ||
| 10 | Linear OA(5105, 132, F5, 58) (dual of [132, 27, 59]-code) | [i] | ||
| 11 | Linear OA(5104, 131, F5, 57) (dual of [131, 27, 58]-code) | [i] | ||
| 12 | Linear OA(5102, 129, F5, 55) (dual of [129, 27, 56]-code) | [i] | ||
| 13 | Linear OA(5101, 128, F5, 54) (dual of [128, 27, 55]-code) | [i] | ||
| 14 | Linear OA(5100, 127, F5, 53) (dual of [127, 27, 54]-code) | [i] | ||
| 15 | Linear OA(5120, 149, F5, 69) (dual of [149, 29, 70]-code) | [i] | Varšamov–Edel Lengthening | |
| 16 | Linear OA(5121, 151, F5, 69) (dual of [151, 30, 70]-code) | [i] | ||