Information on Result #895693
Linear OOA(4217, 4194815, F4, 2, 21) (dual of [(4194815, 2), 8389413, 22]-NRT-code), using (u, u+v)-construction based on
- linear OOA(436, 514, F4, 2, 10) (dual of [(514, 2), 992, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(436, 1028, F4, 10) (dual of [1028, 992, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(436, 1029, F4, 10) (dual of [1029, 993, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(436, 1024, F4, 10) (dual of [1024, 988, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(431, 1024, F4, 9) (dual of [1024, 993, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(40, 5, F4, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(436, 1029, F4, 10) (dual of [1029, 993, 11]-code), using
- OOA 2-folding [i] based on linear OA(436, 1028, F4, 10) (dual of [1028, 992, 11]-code), using
- linear OOA(4181, 4194301, F4, 2, 21) (dual of [(4194301, 2), 8388421, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4181, 8388602, F4, 21) (dual of [8388602, 8388421, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4181, large, F4, 21) (dual of [large, large−181, 22]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(4181, large, F4, 21) (dual of [large, large−181, 22]-code), using
- OOA 2-folding [i] based on linear OA(4181, 8388602, F4, 21) (dual of [8388602, 8388421, 22]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(4217, 838962, F4, 22, 21) (dual of [(838962, 22), 18456947, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |