Information on Result #1297368
Linear OA(2205, 222, F2, 88) (dual of [222, 17, 89]-code), using construction X with Varšamov bound based on
- linear OA(2190, 206, F2, 88) (dual of [206, 16, 89]-code), using
- 1 times truncation [i] based on linear OA(2191, 207, F2, 89) (dual of [207, 16, 90]-code), using
- concatenation of two codes [i] based on
- linear OA(461, 69, F4, 44) (dual of [69, 8, 45]-code), using
- construction XX applied to C([1,140]) ⊂ C([1,128]) ⊂ C([1,125]) [i] based on
- linear OA(459, 63, F4, 46) (dual of [63, 4, 47]-code), using contraction [i] based on linear OA(4185, 189, F4, 140) (dual of [189, 4, 141]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,140], and designed minimum distance d ≥ |I|+1 = 141 [i]
- linear OA(456, 63, F4, 42) (dual of [63, 7, 43]-code), using contraction [i] based on linear OA(4182, 189, F4, 128) (dual of [189, 7, 129]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,128], and designed minimum distance d ≥ |I|+1 = 129 [i]
- linear OA(455, 63, F4, 41) (dual of [63, 8, 42]-code), using contraction [i] based on linear OA(4181, 189, F4, 125) (dual of [189, 8, 126]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,125], and designed minimum distance d ≥ |I|+1 = 126 [i]
- linear OA(41, 5, F4, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to C([1,140]) ⊂ C([1,128]) ⊂ C([1,125]) [i] based on
- linear OA(21, 3, F2, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(461, 69, F4, 44) (dual of [69, 8, 45]-code), using
- concatenation of two codes [i] based on
- 1 times truncation [i] based on linear OA(2191, 207, F2, 89) (dual of [207, 16, 90]-code), using
- linear OA(2190, 207, F2, 73) (dual of [207, 17, 74]-code), using Gilbert–Varšamov bound and bm = 2190 > Vbs−1(k−1) = 959 402652 105028 831936 223186 016401 439035 278393 623772 371553 [i]
- linear OA(214, 15, F2, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,2)), using
- dual of repetition code with length 15 [i]
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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
None.