Information on Result #613729

Linear OA(531, 63, F5, 16) (dual of [63, 32, 17]-code), using an extension Ce(15) of the narrow-sense BCH-code C(I) with length 62 | 53−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16

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:

ResultThis
result
only		Method
1Linear OA(531, 63, F5, 15) (dual of [63, 32, 16]-code) [i]Strength Reduction
2Linear OA(531, 63, F5, 14) (dual of [63, 32, 15]-code) [i]
3Linear OA(532, 64, F5, 16) (dual of [64, 32, 17]-code) [i]Code Embedding in Larger Space
4Linear OA(529, 61, F5, 14) (dual of [61, 32, 15]-code) [i]Truncation
5Linear OA(528, 60, F5, 13) (dual of [60, 32, 14]-code) [i]
6Linear OA(533, 67, F5, 16) (dual of [67, 34, 17]-code) [i]VarÅ¡amov–Edel Lengthening
7Linear OA(535, 77, F5, 16) (dual of [77, 42, 17]-code) [i]
8Linear OA(534, 66, F5, 17) (dual of [66, 32, 18]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
9Linear OA(534, 69, F5, 16) (dual of [69, 35, 17]-code) [i]✔
10Linear OA(538, 70, F5, 18) (dual of [70, 32, 19]-code) [i]✔
11Linear OA(539, 69, F5, 19) (dual of [69, 30, 20]-code) [i]✔
12Linear OA(540, 72, F5, 19) (dual of [72, 32, 20]-code) [i]✔
13Linear OA(536, 74, F5, 16) (dual of [74, 38, 17]-code) [i]✔
14Linear OA(533, 69, F5, 14) (dual of [69, 36, 15]-code) [i]✔
15Linear OA(544, 76, F5, 20) (dual of [76, 32, 21]-code) [i]✔
16Linear OA(538, 71, F5, 17) (dual of [71, 33, 18]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
17Linear OA(534, 70, F5, 15) (dual of [70, 36, 16]-code) [i]✔
18Linear OA(533, 66, F5, 16) (dual of [66, 33, 17]-code) [i]Construction X with VarÅ¡amov Bound
19Linear OOA(531, 21, F5, 3, 16) (dual of [(21, 3), 32, 17]-NRT-code) [i]OOA Folding