Information on Result #737223
Linear OA(4220, 65605, F4, 34) (dual of [65605, 65385, 35]-code), using construction X applied to Ce(33) ⊂ Ce(24) based on
- 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(4145, 65536, F4, 25) (dual of [65536, 65391, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(419, 69, F4, 8) (dual of [69, 50, 9]-code), using
- construction XX applied to C1 = C({0,1,2,3,5,47}), C2 = C([0,6]), C3 = C1 + C2 = C([0,5]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,47}) [i] based on
- linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,47}, and minimum distance d ≥ |{−1,0,…,5}|+1 = 8 (BCH-bound) [i]
- linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(419, 63, F4, 8) (dual of [63, 44, 9]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,47}, and minimum distance d ≥ |{−1,0,…,6}|+1 = 9 (BCH-bound) [i]
- linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(40, 3, F4, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(40, 3, F4, 0) (dual of [3, 3, 1]-code) (see above)
- construction XX applied to C1 = C({0,1,2,3,5,47}), C2 = C([0,6]), C3 = C1 + C2 = C([0,5]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,47}) [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 OOA(4220, 56222, F4, 2, 34) (dual of [(56222, 2), 112224, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4220, 56222, F4, 3, 34) (dual of [(56222, 3), 168446, 35]-NRT-code) | [i] | ||
| 3 | Digital (186, 220, 56222)-net over F4 | [i] | ||
| 4 | Linear OOA(4220, 32802, F4, 2, 34) (dual of [(32802, 2), 65384, 35]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4220, 21868, F4, 3, 34) (dual of [(21868, 3), 65384, 35]-NRT-code) | [i] | ||
| 6 | Linear OOA(4220, 3859, F4, 34, 34) (dual of [(3859, 34), 130986, 35]-NRT-code) | [i] | OA Folding and Stacking | |