Information on Result #895696
Linear OOA(4220, 4194821, F4, 2, 21) (dual of [(4194821, 2), 8389422, 22]-NRT-code), using (u, u+v)-construction based on
- linear OOA(439, 520, F4, 2, 10) (dual of [(520, 2), 1001, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(439, 1040, F4, 10) (dual of [1040, 1001, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(439, 1041, F4, 10) (dual of [1041, 1002, 11]-code), using
- construction XX applied to C1 = C([333,341]), C2 = C([336,342]), C3 = C1 + C2 = C([336,341]), and C∩ = C1 ∩ C2 = C([333,342]) [i] based on
- linear OA(431, 1023, F4, 9) (dual of [1023, 992, 10]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {333,334,…,341}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(426, 1023, F4, 7) (dual of [1023, 997, 8]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {336,337,…,342}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(436, 1023, F4, 10) (dual of [1023, 987, 11]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {333,334,…,342}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(421, 1023, F4, 6) (dual of [1023, 1002, 7]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {336,337,…,341}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(43, 13, F4, 2) (dual of [13, 10, 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
- linear OA(40, 5, F4, 0) (dual of [5, 5, 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
- construction XX applied to C1 = C([333,341]), C2 = C([336,342]), C3 = C1 + C2 = C([336,341]), and C∩ = C1 ∩ C2 = C([333,342]) [i] based on
- discarding factors / shortening the dual code based on linear OA(439, 1041, F4, 10) (dual of [1041, 1002, 11]-code), using
- OOA 2-folding [i] based on linear OA(439, 1040, F4, 10) (dual of [1040, 1001, 11]-code), using
- linear OOA(4181, 4194301, F4, 2, 21) (dual of [(4194301, 2), 8388421, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4181, 8388602, F4, 21) (dual of [8388602, 8388421, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4181, large, F4, 21) (dual of [large, large−181, 22]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(4181, large, F4, 21) (dual of [large, large−181, 22]-code), using
- OOA 2-folding [i] based on linear OA(4181, 8388602, F4, 21) (dual of [8388602, 8388421, 22]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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, 838964, F4, 22, 21) (dual of [(838964, 22), 18456988, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |