Information on Result #896166
Linear OOA(5120, 4194617, F5, 2, 13) (dual of [(4194617, 2), 8389114, 14]-NRT-code), using (u, u+v)-construction based on
- linear OOA(519, 316, F5, 2, 6) (dual of [(316, 2), 613, 7]-NRT-code), using
- OOA 2-folding [i] based on linear OA(519, 632, F5, 6) (dual of [632, 613, 7]-code), using
- construction XX applied to Ce(5) ⊂ Ce(3) ⊂ Ce(2) [i] based on
- linear OA(517, 625, F5, 6) (dual of [625, 608, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(513, 625, F5, 4) (dual of [625, 612, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(59, 625, F5, 3) (dual of [625, 616, 4]-code or 625-cap in PG(8,5)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(51, 6, F5, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(5) ⊂ Ce(3) ⊂ Ce(2) [i] based on
- OOA 2-folding [i] based on linear OA(519, 632, F5, 6) (dual of [632, 613, 7]-code), using
- linear OOA(5101, 4194301, F5, 2, 13) (dual of [(4194301, 2), 8388501, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5101, 8388602, F5, 13) (dual of [8388602, 8388501, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(5101, large, F5, 13) (dual of [large, large−101, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 520−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(5101, large, F5, 13) (dual of [large, large−101, 14]-code), using
- OOA 2-folding [i] based on linear OA(5101, 8388602, F5, 13) (dual of [8388602, 8388501, 14]-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
None.