Information on Result #737263
Linear OA(4211, 16454, F4, 37) (dual of [16454, 16243, 38]-code), using construction X applied to Ce(36) ⊂ Ce(26) based on
- linear OA(4190, 16384, F4, 37) (dual of [16384, 16194, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(4141, 16384, F4, 27) (dual of [16384, 16243, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(421, 70, F4, 9) (dual of [70, 49, 10]-code), using
- construction XX applied to Ce(8) ⊂ Ce(6) ⊂ Ce(5) [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(413, 64, F4, 6) (dual of [64, 51, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(41, 5, F4, 1) (dual of [5, 4, 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
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(8) ⊂ Ce(6) ⊂ Ce(5) [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(4213, 16456, F4, 37) (dual of [16456, 16243, 38]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4210, 16453, F4, 36) (dual of [16453, 16243, 37]-code) | [i] | Truncation | |
| 3 | Linear OOA(4211, 16454, F4, 2, 37) (dual of [(16454, 2), 32697, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(4211, 16454, F4, 3, 37) (dual of [(16454, 3), 49151, 38]-NRT-code) | [i] | ||
| 5 | Digital (174, 211, 16454)-net over F4 | [i] | ||
| 6 | Linear OOA(4211, 8227, F4, 2, 37) (dual of [(8227, 2), 16243, 38]-NRT-code) | [i] | OOA Folding | |