Information on Result #1299618
Linear OA(3240, 280, F3, 114) (dual of [280, 40, 115]-code), using construction X with Varšamov bound based on
- linear OA(3237, 275, F3, 114) (dual of [275, 38, 115]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(3206, 238, F3, 116) (dual of [238, 32, 117]-code), using
- 6 times truncation [i] based on linear OA(3212, 244, F3, 122) (dual of [244, 32, 123]-code), using
- construction X applied to Ce(121) ⊂ Ce(120) [i] based on
- linear OA(3212, 243, F3, 122) (dual of [243, 31, 123]-code), using an extension Ce(121) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,121], and designed minimum distance d ≥ |I|+1 = 122 [i]
- linear OA(3211, 243, F3, 121) (dual of [243, 32, 122]-code), using an extension Ce(120) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,120], and designed minimum distance d ≥ |I|+1 = 121 [i]
- linear OA(30, 1, F3, 0) (dual of [1, 1, 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(121) ⊂ Ce(120) [i] based on
- 6 times truncation [i] based on linear OA(3212, 244, F3, 122) (dual of [244, 32, 123]-code), using
- linear OA(3206, 244, F3, 96) (dual of [244, 38, 97]-code), using Gilbert–Varšamov bound and bm = 3206 > Vbs−1(k−1) = 126 497482 933929 517534 377810 297700 813943 241533 552179 479511 021737 159545 209019 657335 582447 304873 293915 [i]
- linear OA(325, 31, F3, 17) (dual of [31, 6, 18]-code), using
- construction XX applied to C1 = C([0,27]), C2 = C([1,33]), C3 = C1 + C2 = C([1,27]), and C∩ = C1 ∩ C2 = C([0,33]) [i] based on
- linear OA(320, 26, F3, 14) (dual of [26, 6, 15]-code), using contraction [i] based on linear OA(346, 52, F3, 29) (dual of [52, 6, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 52 | 36−1, defining interval I = [0,27], and minimum distance d ≥ |{−1,0,…,27}|+1 = 30 (BCH-bound) [i]
- linear OA(322, 26, F3, 16) (dual of [26, 4, 17]-code), using contraction [i] based on linear OA(348, 52, F3, 33) (dual of [52, 4, 34]-code), using the narrow-sense BCH-code C(I) with length 52 | 36−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(323, 26, F3, 17) (dual of [26, 3, 18]-code), using contraction [i] based on linear OA(349, 52, F3, 35) (dual of [52, 3, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 52 | 36−1, defining interval I = [0,33], and minimum distance d ≥ |{−1,0,…,33}|+1 = 36 (BCH-bound) [i]
- linear OA(319, 26, F3, 13) (dual of [26, 7, 14]-code), using contraction [i] based on linear OA(345, 52, F3, 27) (dual of [52, 7, 28]-code), using the narrow-sense BCH-code C(I) with length 52 | 36−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- linear OA(32, 4, F3, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
- extended Reed–Solomon code RSe(2,3) [i]
- Hamming code H(2,3) [i]
- Simplex code S(2,3) [i]
- the Tetracode [i]
- construction XX applied to C1 = C([0,27]), C2 = C([1,33]), C3 = C1 + C2 = C([1,27]), and C∩ = C1 ∩ C2 = C([0,33]) [i] based on
- linear OA(3206, 238, F3, 116) (dual of [238, 32, 117]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(3237, 277, F3, 112) (dual of [277, 40, 113]-code), using Gilbert–Varšamov bound and bm = 3237 > Vbs−1(k−1) = 113301 952507 713802 706355 880940 340389 096921 823678 088817 479548 356179 355509 728407 410095 139624 055679 119115 094611 087249 [i]
- linear OA(31, 3, F3, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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 OA(3241, 282, F3, 114) (dual of [282, 41, 115]-code) | [i] | Construction X with Varšamov Bound | |