Information on Result #1607162
Linear OOA(3181, 4194566, F3, 4, 16) (dual of [(4194566, 4), 16778083, 17]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3181, 4194566, F3, 2, 16) (dual of [(4194566, 2), 8388951, 17]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(330, 265, F3, 2, 8) (dual of [(265, 2), 500, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(330, 265, F3, 8) (dual of [265, 235, 9]-code), using
- 13 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 0, 0, 0, 1, 6 times 0) [i] based on linear OA(326, 248, F3, 8) (dual of [248, 222, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(326, 243, F3, 8) (dual of [243, 217, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(321, 243, F3, 7) (dual of [243, 222, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(30, 5, F3, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- 13 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 0, 0, 0, 1, 6 times 0) [i] based on linear OA(326, 248, F3, 8) (dual of [248, 222, 9]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(330, 265, F3, 8) (dual of [265, 235, 9]-code), using
- linear OOA(3151, 4194301, F3, 2, 16) (dual of [(4194301, 2), 8388451, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3151, 8388602, F3, 16) (dual of [8388602, 8388451, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3151, large, F3, 16) (dual of [large, large−151, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(3151, large, F3, 16) (dual of [large, large−151, 17]-code), using
- OOA 2-folding [i] based on linear OA(3151, 8388602, F3, 16) (dual of [8388602, 8388451, 17]-code), using
- linear OOA(330, 265, F3, 2, 8) (dual of [(265, 2), 500, 9]-NRT-code), using
Mode: 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(3181, 2097282, F3, 20, 16) (dual of [(2097282, 20), 41945459, 17]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |