Information on Result #701159
Linear OA(59, 28, F5, 5) (dual of [28, 19, 6]-code), using construction XX applied to C1 = C({0,1,2,19}), C2 = C([0,3]), C3 = C1 + C2 = C([0,2]), and C∩ = C1 ∩ C2 = C({0,1,2,3,19}) based on
- linear OA(57, 24, F5, 4) (dual of [24, 17, 5]-code), using the primitive cyclic code C(A) with length 24 = 52−1, defining set A = {0,1,2,19}, and minimum distance d ≥ |{−1,0,1,2}|+1 = 5 (BCH-bound) [i]
- 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]
- linear OA(59, 24, F5, 5) (dual of [24, 15, 6]-code), using the primitive cyclic code C(A) with length 24 = 52−1, defining set A = {0,1,2,3,19}, and minimum distance d ≥ |{−1,0,1,2,3}|+1 = 6 (BCH-bound) [i]
- linear OA(55, 24, F5, 3) (dual of [24, 19, 4]-code or 24-cap in PG(4,5)), using the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(50, 2, F5, 0) (dual of [2, 2, 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, 2, F5, 0) (dual of [2, 2, 1]-code) (see above)
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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(563, 657, F5, 17) (dual of [657, 594, 18]-code) | [i] | Construction XX with Cyclic Codes | |
| 2 | Linear OA(566, 656, F5, 18) (dual of [656, 590, 19]-code) | [i] | ||
| 3 | Linear OA(571, 661, F5, 19) (dual of [661, 590, 20]-code) | [i] | ||
| 4 | Linear OA(577, 667, F5, 20) (dual of [667, 590, 21]-code) | [i] | ||
| 5 | Linear OA(575, 661, F5, 20) (dual of [661, 586, 21]-code) | [i] | ||
| 6 | Linear OA(582, 668, F5, 22) (dual of [668, 586, 23]-code) | [i] | ||
| 7 | Linear OA(579, 657, F5, 22) (dual of [657, 578, 23]-code) | [i] | ||
| 8 | Linear OA(586, 668, F5, 23) (dual of [668, 582, 24]-code) | [i] | ||
| 9 | Linear OA(582, 656, F5, 23) (dual of [656, 574, 24]-code) | [i] | ||
| 10 | Linear OA(590, 668, F5, 24) (dual of [668, 578, 25]-code) | [i] | ||
| 11 | Linear OA(587, 661, F5, 24) (dual of [661, 574, 25]-code) | [i] | ||
| 12 | Linear OA(593, 667, F5, 25) (dual of [667, 574, 26]-code) | [i] | ||
| 13 | Linear OA(591, 661, F5, 25) (dual of [661, 570, 26]-code) | [i] | ||
| 14 | Linear OA(598, 668, F5, 27) (dual of [668, 570, 28]-code) | [i] | ||
| 15 | Linear OA(595, 657, F5, 27) (dual of [657, 562, 28]-code) | [i] | ||
| 16 | Linear OA(5102, 668, F5, 28) (dual of [668, 566, 29]-code) | [i] | ||
| 17 | Linear OA(5114, 668, F5, 32) (dual of [668, 554, 33]-code) | [i] | ||
| 18 | Linear OA(5121, 679, F5, 33) (dual of [679, 558, 34]-code) | [i] | ||
| 19 | Linear OA(5118, 672, F5, 33) (dual of [672, 554, 34]-code) | [i] | ||
| 20 | Linear OA(5116, 666, F5, 33) (dual of [666, 550, 34]-code) | [i] | ||
| 21 | Linear OA(5112, 654, F5, 33) (dual of [654, 542, 34]-code) | [i] | ||
| 22 | Linear OA(5122, 672, F5, 34) (dual of [672, 550, 35]-code) | [i] | ||
| 23 | Linear OA(5117, 659, F5, 34) (dual of [659, 542, 35]-code) | [i] | ||
| 24 | Linear OA(5116, 656, F5, 34) (dual of [656, 540, 35]-code) | [i] | ||
| 25 | Linear OA(5126, 672, F5, 35) (dual of [672, 546, 36]-code) | [i] | ||
| 26 | Linear OA(5123, 665, F5, 35) (dual of [665, 542, 36]-code) | [i] | ||
| 27 | Linear OA(5121, 661, F5, 35) (dual of [661, 540, 36]-code) | [i] | ||
| 28 | Linear OA(5130, 672, F5, 37) (dual of [672, 542, 38]-code) | [i] | ||
| 29 | Linear OA(5128, 668, F5, 37) (dual of [668, 540, 38]-code) | [i] | ||
| 30 | Linear OA(5125, 657, F5, 37) (dual of [657, 532, 38]-code) | [i] | ||
| 31 | Linear OA(5132, 668, F5, 38) (dual of [668, 536, 39]-code) | [i] | ||
| 32 | Linear OA(5128, 656, F5, 38) (dual of [656, 528, 39]-code) | [i] | ||
| 33 | Linear OA(5134, 672, F5, 38) (dual of [672, 538, 39]-code) | [i] | ||
| 34 | Linear OA(5136, 668, F5, 39) (dual of [668, 532, 40]-code) | [i] | ||
| 35 | Linear OA(5133, 661, F5, 39) (dual of [661, 528, 40]-code) | [i] | ||
| 36 | Linear OA(5139, 667, F5, 40) (dual of [667, 528, 41]-code) | [i] | ||
| 37 | Linear OA(5137, 661, F5, 40) (dual of [661, 524, 41]-code) | [i] | ||
| 38 | Linear OA(5147, 675, F5, 42) (dual of [675, 528, 43]-code) | [i] | ||
| 39 | Linear OA(5144, 668, F5, 42) (dual of [668, 524, 43]-code) | [i] | ||
| 40 | Linear OA(5141, 657, F5, 42) (dual of [657, 516, 43]-code) | [i] | ||
| 41 | Linear OA(5146, 672, F5, 42) (dual of [672, 526, 43]-code) | [i] | ||
| 42 | Linear OA(5148, 668, F5, 43) (dual of [668, 520, 44]-code) | [i] | ||
| 43 | Linear OA(5144, 656, F5, 43) (dual of [656, 512, 44]-code) | [i] | ||
| 44 | Linear OA(5150, 672, F5, 43) (dual of [672, 522, 44]-code) | [i] | ||
| 45 | Linear OA(5149, 661, F5, 44) (dual of [661, 512, 45]-code) | [i] | ||