Information on Result #1014649
Linear OOA(8172, 6291455, F8, 3, 16) (dual of [(6291455, 3), 18874193, 17]-NRT-code), using (u, u+v)-construction based on
- linear OOA(850, 699053, F8, 3, 8) (dual of [(699053, 3), 2097109, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(850, 2097159, F8, 8) (dual of [2097159, 2097109, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(850, 2097160, F8, 8) (dual of [2097160, 2097110, 9]-code), using
- construction X4 applied to C([1,8]) ⊂ C([1,6]) [i] based on
- linear OA(849, 2097151, F8, 8) (dual of [2097151, 2097102, 9]-code), using the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(842, 2097151, F8, 6) (dual of [2097151, 2097109, 7]-code), using the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(88, 9, F8, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,8)), using
- dual of repetition code with length 9 [i]
- linear OA(81, 9, F8, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- construction X4 applied to C([1,8]) ⊂ C([1,6]) [i] based on
- discarding factors / shortening the dual code based on linear OA(850, 2097160, F8, 8) (dual of [2097160, 2097110, 9]-code), using
- OOA 3-folding [i] based on linear OA(850, 2097159, F8, 8) (dual of [2097159, 2097109, 9]-code), using
- linear OOA(8122, 5592402, F8, 3, 16) (dual of [(5592402, 3), 16777084, 17]-NRT-code), using
- trace code [i] based on linear OOA(6461, 2796201, F64, 3, 16) (dual of [(2796201, 3), 8388542, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6461, large, F64, 16) (dual of [large, large−61, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- OOA 3-folding [i] based on linear OA(6461, large, F64, 16) (dual of [large, large−61, 17]-code), using
- trace code [i] based on linear OOA(6461, 2796201, F64, 3, 16) (dual of [(2796201, 3), 8388542, 17]-NRT-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(8172, 2097151, F8, 21, 16) (dual of [(2097151, 21), 44039999, 17]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |