Information on Result #737355
Linear OA(4195, 4164, F4, 39) (dual of [4164, 3969, 40]-code), using construction X applied to Ce(38) ⊂ Ce(28) based on
- linear OA(4175, 4096, F4, 39) (dual of [4096, 3921, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(4127, 4096, F4, 29) (dual of [4096, 3969, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(420, 68, F4, 9) (dual of [68, 48, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(419, 64, F4, 9) (dual of [64, 45, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(416, 64, F4, 7) (dual of [64, 48, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(8) ⊂ Ce(6) [i] based on
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(4196, 4165, F4, 39) (dual of [4165, 3969, 40]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4198, 4167, F4, 39) (dual of [4167, 3969, 40]-code) | [i] | ||
| 3 | Linear OA(4199, 4168, F4, 39) (dual of [4168, 3969, 40]-code) | [i] | ||
| 4 | Linear OA(4200, 4169, F4, 39) (dual of [4169, 3969, 40]-code) | [i] | ||
| 5 | Linear OA(4201, 4170, F4, 39) (dual of [4170, 3969, 40]-code) | [i] | ||
| 6 | Linear OA(4202, 4171, F4, 39) (dual of [4171, 3969, 40]-code) | [i] | ||
| 7 | Linear OOA(4195, 2082, F4, 2, 39) (dual of [(2082, 2), 3969, 40]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(4195, 1388, F4, 3, 39) (dual of [(1388, 3), 3969, 40]-NRT-code) | [i] | ||