Information on Result #678814
Linear OA(4221, 65557, F4, 37) (dual of [65557, 65336, 38]-code), using construction XX applied to Ce(36) ⊂ Ce(33) ⊂ Ce(32) based on
- linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(4201, 65536, F4, 34) (dual of [65536, 65335, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(4193, 65536, F4, 33) (dual of [65536, 65343, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(43, 20, F4, 2) (dual of [20, 17, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- linear OA(40, 1, F4, 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 OOA(4221, 32778, F4, 2, 37) (dual of [(32778, 2), 65335, 38]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4221, 21852, F4, 3, 37) (dual of [(21852, 3), 65335, 38]-NRT-code) | [i] | ||
| 3 | Linear OOA(4221, 3642, F4, 37, 37) (dual of [(3642, 37), 134533, 38]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |