Information on Result #1017299
Linear OOA(4943, 39317, F49, 3, 12) (dual of [(39317, 3), 117908, 13]-NRT-code), using (u, u+v)-construction based on
- linear OOA(499, 100, F49, 3, 6) (dual of [(100, 3), 291, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(493, 50, F49, 3, 3) (dual of [(50, 3), 147, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;147,49) [i]
- linear OOA(496, 50, F49, 3, 6) (dual of [(50, 3), 144, 7]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;144,49) [i]
- linear OOA(493, 50, F49, 3, 3) (dual of [(50, 3), 147, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(4934, 39217, F49, 3, 12) (dual of [(39217, 3), 117617, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4934, 117651, F49, 12) (dual of [117651, 117617, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(4934, 117652, F49, 12) (dual of [117652, 117618, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(4934, 117649, F49, 12) (dual of [117649, 117615, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(4931, 117649, F49, 11) (dual of [117649, 117618, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(490, 3, F49, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(4934, 117652, F49, 12) (dual of [117652, 117618, 13]-code), using
- OOA 3-folding [i] based on linear OA(4934, 117651, F49, 12) (dual of [117651, 117617, 13]-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 OOA(4943, 19658, F49, 15, 12) (dual of [(19658, 15), 294827, 13]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |