Information on Result #896221
Linear OOA(5148, 4194620, F5, 2, 16) (dual of [(4194620, 2), 8389092, 17]-NRT-code), using (u, u+v)-construction based on
- linear OOA(527, 319, F5, 2, 8) (dual of [(319, 2), 611, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(527, 638, F5, 8) (dual of [638, 611, 9]-code), using
- construction XX applied to C1 = C([622,3]), C2 = C([0,5]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C([622,5]) [i] based on
- linear OA(521, 624, F5, 6) (dual of [624, 603, 7]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−2,−1,…,3}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(517, 624, F5, 6) (dual of [624, 607, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(525, 624, F5, 8) (dual of [624, 599, 9]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−2,−1,…,5}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(513, 624, F5, 4) (dual of [624, 611, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(51, 9, F5, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(51, 5, F5, 1) (dual of [5, 4, 2]-code), using
- Reed–Solomon code RS(4,5) [i]
- construction XX applied to C1 = C([622,3]), C2 = C([0,5]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C([622,5]) [i] based on
- OOA 2-folding [i] based on linear OA(527, 638, F5, 8) (dual of [638, 611, 9]-code), using
- linear OOA(5121, 4194301, F5, 2, 16) (dual of [(4194301, 2), 8388481, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5121, 8388602, F5, 16) (dual of [8388602, 8388481, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(5121, large, F5, 16) (dual of [large, large−121, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(5121, large, F5, 16) (dual of [large, large−121, 17]-code), using
- OOA 2-folding [i] based on linear OA(5121, 8388602, F5, 16) (dual of [8388602, 8388481, 17]-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(5149, 4194620, F5, 2, 16) (dual of [(4194620, 2), 8389091, 17]-NRT-code) | [i] | OOA Duplication | |