Information on Result #1436970
Linear OOA(565, 855, F5, 2, 18) (dual of [(855, 2), 1645, 19]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(565, 855, F5, 18) (dual of [855, 790, 19]-code), using
- 215 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 5 times 0, 1, 11 times 0, 1, 24 times 0, 1, 40 times 0, 1, 57 times 0, 1, 70 times 0) [i] based on linear OA(557, 632, F5, 18) (dual of [632, 575, 19]-code), using
- construction XX applied to C1 = C([623,15]), C2 = C([0,16]), C3 = C1 + C2 = C([0,15]), and C∩ = C1 ∩ C2 = C([623,16]) [i] based on
- linear OA(553, 624, F5, 17) (dual of [624, 571, 18]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−1,0,…,15}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(553, 624, F5, 17) (dual of [624, 571, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(557, 624, F5, 18) (dual of [624, 567, 19]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−1,0,…,16}, and designed minimum distance d ≥ |I|+1 = 19 [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(50, 4, F5, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(50, 4, F5, 0) (dual of [4, 4, 1]-code) (see above)
- construction XX applied to C1 = C([623,15]), C2 = C([0,16]), C3 = C1 + C2 = C([0,15]), and C∩ = C1 ∩ C2 = C([623,16]) [i] based on
Mode: 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(565, 427, F5, 3, 18) (dual of [(427, 3), 1216, 19]-NRT-code) | [i] | OOA Folding | |