Information on Result #1453317
Linear OOA(1651, 131090, F16, 2, 12) (dual of [(131090, 2), 262129, 13]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(1651, 131090, F16, 12) (dual of [131090, 131039, 13]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(1650, 131088, F16, 12) (dual of [131088, 131038, 13]-code), using
- trace code [i] based on linear OA(25625, 65544, F256, 12) (dual of [65544, 65519, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- linear OA(25623, 65536, F256, 12) (dual of [65536, 65513, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(25617, 65536, F256, 9) (dual of [65536, 65519, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(2562, 8, F256, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- Reed–Solomon code RS(254,256) [i]
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- trace code [i] based on linear OA(25625, 65544, F256, 12) (dual of [65544, 65519, 13]-code), using
- linear OA(1650, 131089, F16, 11) (dual of [131089, 131039, 12]-code), using Gilbert–Varšamov bound and bm = 1650 > Vbs−1(k−1) = 238 030195 374032 030705 784269 317830 412494 336250 444404 605371 [i]
- linear OA(160, 1, F16, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(1650, 131088, F16, 12) (dual of [131088, 131038, 13]-code), using
Mode: 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(1651, 43696, F16, 14, 12) (dual of [(43696, 14), 611693, 13]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |