Information on Result #900728
Linear OOA(27110, 4460061, F27, 2, 16) (dual of [(4460061, 2), 8920012, 17]-NRT-code), using (u, u+v)-construction based on
- linear OOA(2734, 265760, F27, 2, 8) (dual of [(265760, 2), 531486, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(275, 38, F27, 2, 4) (dual of [(38, 2), 71, 5]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,71P) [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- linear OOA(2729, 265722, F27, 2, 8) (dual of [(265722, 2), 531415, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2729, 531444, F27, 8) (dual of [531444, 531415, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(2729, 531445, F27, 8) (dual of [531445, 531416, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(2729, 531441, F27, 8) (dual of [531441, 531412, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(2725, 531441, F27, 7) (dual of [531441, 531416, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(270, 4, F27, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(2729, 531445, F27, 8) (dual of [531445, 531416, 9]-code), using
- OOA 2-folding [i] based on linear OA(2729, 531444, F27, 8) (dual of [531444, 531415, 9]-code), using
- linear OOA(275, 38, F27, 2, 4) (dual of [(38, 2), 71, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2776, 4194301, F27, 2, 16) (dual of [(4194301, 2), 8388526, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2776, 8388602, F27, 16) (dual of [8388602, 8388526, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2776, large, F27, 16) (dual of [large, large−76, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(2776, large, F27, 16) (dual of [large, large−76, 17]-code), using
- OOA 2-folding [i] based on linear OA(2776, 8388602, F27, 16) (dual of [8388602, 8388526, 17]-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(27110, 1115015, F27, 18, 16) (dual of [(1115015, 18), 20070160, 17]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |