Information on Result #732128
Linear OA(1672, 1048840, F16, 13) (dual of [1048840, 1048768, 14]-code), using (u, u+v)-construction based on
- linear OA(1611, 259, F16, 6) (dual of [259, 248, 7]-code), using
- construction XX applied to C1 = C([254,3]), C2 = C([0,4]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C([254,4]) [i] based on
- linear OA(169, 255, F16, 5) (dual of [255, 246, 6]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−1,0,1,2,3}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(169, 255, F16, 5) (dual of [255, 246, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(1611, 255, F16, 6) (dual of [255, 244, 7]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−1,0,…,4}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(167, 255, F16, 4) (dual of [255, 248, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(160, 2, F16, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(160, 2, F16, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([254,3]), C2 = C([0,4]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C([254,4]) [i] based on
- linear OA(1661, 1048581, F16, 13) (dual of [1048581, 1048520, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(1661, 1048576, F16, 13) (dual of [1048576, 1048515, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(1656, 1048576, F16, 12) (dual of [1048576, 1048520, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(160, 5, F16, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s (see above)
- construction X applied to Ce(12) ⊂ Ce(11) [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(1672, 524420, F16, 2, 13) (dual of [(524420, 2), 1048768, 14]-NRT-code) | [i] | OOA Folding | |