Information on Result #732905
Linear OA(2534, 682, F25, 13) (dual of [682, 648, 14]-code), using (u, u+v)-construction based on
- linear OA(259, 54, F25, 6) (dual of [54, 45, 7]-code), using
- construction X applied to C([10,15]) ⊂ C([11,15]) [i] based on
- linear OA(259, 52, F25, 6) (dual of [52, 43, 7]-code), using the BCH-code C(I) with length 52 | 252−1, defining interval I = {10,11,…,15}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(257, 52, F25, 5) (dual of [52, 45, 6]-code), using the BCH-code C(I) with length 52 | 252−1, defining interval I = {11,12,13,14,15}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to C([10,15]) ⊂ C([11,15]) [i] based on
- linear OA(2525, 628, F25, 13) (dual of [628, 603, 14]-code), using
- construction XX applied to C1 = C([623,10]), C2 = C([0,11]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([623,11]) [i] based on
- linear OA(2523, 624, F25, 12) (dual of [624, 601, 13]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,10}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(2523, 624, F25, 12) (dual of [624, 601, 13]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(2525, 624, F25, 13) (dual of [624, 599, 14]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,11}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2521, 624, F25, 11) (dual of [624, 603, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code) (see above)
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([623,10]), C2 = C([0,11]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([623,11]) [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(2534, 341, F25, 2, 13) (dual of [(341, 2), 648, 14]-NRT-code) | [i] | OOA Folding | |