Information on Result #823690
Linear OOA(4109, 8200, F4, 2, 21) (dual of [(8200, 2), 16291, 22]-NRT-code), using OOA 2-folding based on linear OA(4109, 16400, F4, 21) (dual of [16400, 16291, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4109, 16401, F4, 21) (dual of [16401, 16292, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(17) [i] based on
- linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(492, 16384, F4, 18) (dual of [16384, 16292, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(43, 17, F4, 2) (dual of [17, 14, 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
- construction X applied to Ce(20) ⊂ Ce(17) [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(4109, 8200, F4, 3, 21) (dual of [(8200, 3), 24491, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
2 | Digital (88, 109, 8200)-net over F4 | [i] |