Information on Result #895675
Linear OOA(4217, 4194818, F4, 2, 20) (dual of [(4194818, 2), 8389419, 21]-NRT-code), using (u, u+v)-construction based on
- linear OOA(437, 517, F4, 2, 10) (dual of [(517, 2), 997, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(437, 1034, F4, 10) (dual of [1034, 997, 11]-code), using
- construction XX applied to C1 = C([333,341]), C2 = C([335,342]), C3 = C1 + C2 = C([335,341]), 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(431, 1023, F4, 8) (dual of [1023, 992, 9]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {335,336,…,342}, and designed minimum distance d ≥ |I|+1 = 9 [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(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 = {335,336,…,341}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(41, 6, F4, 1) (dual of [6, 5, 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
- 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([335,342]), C3 = C1 + C2 = C([335,341]), and C∩ = C1 ∩ C2 = C([333,342]) [i] based on
- OOA 2-folding [i] based on linear OA(437, 1034, F4, 10) (dual of [1034, 997, 11]-code), using
- linear OOA(4180, 4194301, F4, 2, 20) (dual of [(4194301, 2), 8388422, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4180, 8388602, F4, 20) (dual of [8388602, 8388422, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(4180, large, F4, 20) (dual of [large, large−180, 21]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(4180, large, F4, 20) (dual of [large, large−180, 21]-code), using
- OOA 2-folding [i] based on linear OA(4180, 8388602, F4, 20) (dual of [8388602, 8388422, 21]-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(4217, 838963, F4, 22, 20) (dual of [(838963, 22), 18456969, 21]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |