Information on Result #701514
Linear OA(769, 80, F7, 45) (dual of [80, 11, 46]-code), using construction XX applied to C1 = C({0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,32,33,34,41}), C2 = C([1,27]), C3 = C1 + C2 = C([1,26]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27,32,33,34,41}) based on
- linear OA(745, 48, F7, 40) (dual of [48, 3, 41]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,32,33,34,41}, and minimum distance d ≥ |{−16,−11,−6,…,−13}|+1 = 41 (BCH-bound) [i]
- linear OA(739, 48, F7, 31) (dual of [48, 9, 32]-code), using the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(747, 48, F7, 47) (dual of [48, 1, 48]-code or 48-arc in PG(46,7)), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27,32,33,34,41}, and minimum distance d ≥ |{3,14,25,…,−19}|+1 = 48 (BCH-bound) [i]
- linear OA(737, 48, F7, 26) (dual of [48, 11, 27]-code), using the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(718, 26, F7, 13) (dual of [26, 8, 14]-code), using
- construction XX applied to C1 = C([0,35]), C2 = C([1,38]), C3 = C1 + C2 = C([1,35]), and C∩ = C1 ∩ C2 = C([0,38]) [i] based on
- linear OA(717, 24, F7, 12) (dual of [24, 7, 13]-code), using contraction [i] based on linear OA(765, 72, F7, 38) (dual of [72, 7, 39]-code), using the expurgated narrow-sense BCH-code C(I) with length 72 | 76−1, defining interval I = [0,35], and minimum distance d ≥ |{−2,−1,…,35}|+1 = 39 (BCH-bound) [i]
- linear OA(717, 24, F7, 12) (dual of [24, 7, 13]-code), using contraction [i] based on linear OA(765, 72, F7, 38) (dual of [72, 7, 39]-code), using the narrow-sense BCH-code C(I) with length 72 | 76−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(718, 24, F7, 13) (dual of [24, 6, 14]-code), using contraction [i] based on linear OA(766, 72, F7, 41) (dual of [72, 6, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 72 | 76−1, defining interval I = [0,38], and minimum distance d ≥ |{−2,−1,…,38}|+1 = 42 (BCH-bound) [i]
- linear OA(716, 24, F7, 11) (dual of [24, 8, 12]-code), using contraction [i] based on linear OA(764, 72, F7, 35) (dual of [72, 8, 36]-code), using the narrow-sense BCH-code C(I) with length 72 | 76−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code) (see above)
- construction XX applied to C1 = C([0,35]), C2 = C([1,38]), C3 = C1 + C2 = C([1,35]), and C∩ = C1 ∩ C2 = C([0,38]) [i] based on
- linear OA(74, 6, F7, 4) (dual of [6, 2, 5]-code or 6-arc in PG(3,7)), using
- discarding factors / shortening the dual code based on linear OA(74, 7, F7, 4) (dual of [7, 3, 5]-code or 7-arc in PG(3,7)), using
- Reed–Solomon code RS(3,7) [i]
- discarding factors / shortening the dual code based on linear OA(74, 7, F7, 4) (dual of [7, 3, 5]-code or 7-arc in PG(3,7)), using
Mode: Constructive and 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.
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Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(769, 40, F7, 2, 45) (dual of [(40, 2), 11, 46]-NRT-code) | [i] | OOA Folding | |