Information on Result #2496622
Linear OOA(4223, 524319, F4, 2, 28) (dual of [(524319, 2), 1048415, 29]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4221, 524318, F4, 2, 28) (dual of [(524318, 2), 1048415, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4221, 1048636, F4, 28) (dual of [1048636, 1048415, 29]-code), using
- construction X applied to Ce(28) ⊂ Ce(21) [i] based on
- linear OA(4211, 1048576, F4, 29) (dual of [1048576, 1048365, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4161, 1048576, F4, 22) (dual of [1048576, 1048415, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(410, 60, F4, 5) (dual of [60, 50, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- construction X applied to Ce(28) ⊂ Ce(21) [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(4223, 524319, F4, 3, 28) (dual of [(524319, 3), 1572734, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (195, 223, 524319)-net over F4 | [i] | ||