Information on Result #682150
Linear OA(5148, 1953146, F5, 21) (dual of [1953146, 1952998, 22]-code), using construction X applied to Ce(20) ⊂ Ce(17) based on
- linear OA(5145, 1953125, F5, 21) (dual of [1953125, 1952980, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(5127, 1953125, F5, 18) (dual of [1953125, 1952998, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(53, 21, F5, 2) (dual of [21, 18, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), 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 OA(5147, 1953145, F5, 20) (dual of [1953145, 1952998, 21]-code) | [i] | Truncation | |
| 2 | Linear OOA(5148, 976573, F5, 2, 21) (dual of [(976573, 2), 1952998, 22]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(5148, 651048, F5, 3, 21) (dual of [(651048, 3), 1952996, 22]-NRT-code) | [i] | ||
| 4 | Linear OOA(5148, 195314, F5, 21, 21) (dual of [(195314, 21), 4101446, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |