Information on Result #711258
Linear OA(581, 656, F5, 23) (dual of [656, 575, 24]-code), using construction XX applied to C1 = C([619,15]), C2 = C([0,17]), C3 = C1 + C2 = C([0,15]), and C∩ = C1 ∩ C2 = C([619,17]) based on
- linear OA(565, 624, F5, 21) (dual of [624, 559, 22]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−5,−4,…,15}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(557, 624, F5, 18) (dual of [624, 567, 19]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(573, 624, F5, 23) (dual of [624, 551, 24]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−5,−4,…,17}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(549, 624, F5, 16) (dual of [624, 575, 17]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(57, 23, F5, 4) (dual of [23, 16, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(57, 24, F5, 4) (dual of [24, 17, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(57, 24, F5, 4) (dual of [24, 17, 5]-code), using
- 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
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(581, 328, F5, 2, 23) (dual of [(328, 2), 575, 24]-NRT-code) | [i] | OOA Folding | |