Information on Result #1544455
Linear OOA(4236, 151650, F4, 3, 33) (dual of [(151650, 3), 454714, 34]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4236, 151650, F4, 33) (dual of [151650, 151414, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(4236, 262218, F4, 33) (dual of [262218, 261982, 34]-code), using
- 2 times code embedding in larger space [i] based on linear OA(4234, 262216, F4, 33) (dual of [262216, 261982, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,12]) [i] based on
- linear OA(4217, 262145, F4, 33) (dual of [262145, 261928, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(4163, 262145, F4, 25) (dual of [262145, 261982, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(417, 71, F4, 7) (dual of [71, 54, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(4) [i] based on
- 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(410, 64, F4, 5) (dual of [64, 54, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(41, 7, F4, 1) (dual of [7, 6, 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
- construction X applied to Ce(6) ⊂ Ce(4) [i] based on
- construction X applied to C([0,16]) ⊂ C([0,12]) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(4234, 262216, F4, 33) (dual of [262216, 261982, 34]-code), using
Mode: 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(4236, 25274, F4, 39, 33) (dual of [(25274, 39), 985450, 34]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |