lower bound: | 102 |
upper bound: | 111 |
Construction of a linear code [177,11,102] over GF(3): [1]: [2, 1, 2] Cyclic Linear Code over GF(3) RepetitionCode of length 2 [2]: [16, 5, 9] Linear Code over GF(3) Construction from a stored generator matrix: [ 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 2, 2, 2, 0, 1, 2 ] [ 0, 1, 0, 1, 0, 0, 2, 0, 2, 1, 0, 0, 1, 2, 1, 2 ] [ 0, 0, 1, 2, 0, 0, 2, 0, 2, 1, 1, 2, 2, 0, 0, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 1, 1, 2, 2, 1, 0, 1, 1, 1 ] [ 0, 0, 0, 0, 0, 1, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1 ] [3]: [15, 4, 9] Linear Code over GF(3) Shortening of [2] at { 16 } [4]: [160, 10, 93] Quasicyclic of degree 2 Linear Code over GF(3) QuasiCyclicCode of length 160 with generating polynomials: 2*x^79 + x^78 + x^76 + 2*x^75 + 2*x^74 + x^72 + 2*x^71 + 2*x^68 + 2*x^66 + 2*x^63 + x^62 + x^61 + x^60 + x^59 + 2*x^58 + 2*x^57 + 2*x^55 + x^53 + 2*x^51 + x^50 + x^49 + x^48 + x^47 + x^46 + x^44 + 2*x^43 + x^42 + 2*x^41 + 2*x^40 + 2*x^36 + x^35 + x^34 + 2*x^33 + 2*x^31 + x^28 + 2*x^26 + x^25 + 2*x^24 + 2*x^23 + 2*x^19 + 2*x^18 + 2*x^17 + x^16 + 2*x^10 + x^7, 2*x^79 + 2*x^77 + x^76 + 2*x^75 + 2*x^73 + 2*x^71 + 2*x^70 + 2*x^69 + 2*x^63 + x^62 + 2*x^61 + x^60 + x^59 + x^58 + 2*x^57 + 2*x^56 + 2*x^55 + x^54 + 2*x^51 + 2*x^50 + x^49 + x^48 + 2*x^47 + x^46 + x^44 + x^43 + 2*x^42 + 2*x^41 + x^40 + x^39 + 2*x^38 + x^37 + x^36 + 2*x^35 + x^33 + 2*x^31 + x^29 + 2*x^27 + 2*x^26 + 2*x^25 + x^24 + 2*x^23 + x^22 + 2*x^20 + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x^10 + 2*x^8 + x^7 + 2*x^6 + x^5 + 2*x^3 + 2*x^2 + x + 2 [5]: [160, 7, 100] Quasicyclic of degree 2 Linear Code over GF(3) QuasiCyclicCode of length 160 with generating polynomials: x^79 + 2*x^78 + x^77 + x^74 + x^73 + x^72 + 2*x^71 + 2*x^70 + x^69 + x^67 + x^66 + x^65 + 2*x^62 + 2*x^61 + x^60 + 2*x^59 + x^57 + 2*x^55 + x^54 + 2*x^53 + 2*x^52 + 2*x^51 + 2*x^50 + x^48 + x^46 + 2*x^44 + x^42 + x^41 + 2*x^39 + 2*x^38 + 2*x^37 + 2*x^36 + x^35 + 2*x^32 + x^31 + 2*x^30 + 2*x^29 + 2*x^28 + 2*x^22 + x^21 + x^20 + 2*x^19 + x^18 + x^15 + x^13 + 2*x^11 + 2*x^10 + x^9 + 2*x^8 + x^3, x^79 + 2*x^78 + x^77 + x^76 + 2*x^74 + x^73 + x^72 + x^71 + 2*x^70 + 2*x^68 + 2*x^65 + 2*x^64 + 2*x^62 + x^60 + 2*x^59 + 2*x^56 + 2*x^55 + x^54 + x^53 + 2*x^52 + 2*x^51 + x^50 + x^47 + 2*x^46 + x^44 + x^40 + x^38 + 2*x^37 + x^30 + 2*x^28 + 2*x^26 + 2*x^25 + 2*x^24 + x^23 + x^22 + x^19 + 2*x^18 + x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + 2*x^12 + x^11 + x^10 + x^9 + x^8 + x^6 + 2*x^2 + x [6]: [160, 11, 91] Quasicyclic of degree 2 Linear Code over GF(3) QuasiCyclicCode of length 160 with generating polynomials: x^79 + 2*x^78 + 2*x^76 + x^75 + x^74 + 2*x^73 + x^71 + 2*x^70 + x^69 + x^67 + x^66 + 2*x^64 + x^63 + x^62 + x^60 + x^57 + x^54 + 2*x^51 + x^50 + x^49 + x^48 + x^47 + x^44 + x^43 + 2*x^40 + 2*x^39 + 2*x^38 + x^37 + 2*x^35 + 2*x^33 + x^30 + x^29 + x^28 + x^27 + 2*x^25 + 2*x^23 + x^22 + x^21 + x^20 + x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^4, 2*x^78 + x^77 + 2*x^76 + 2*x^74 + x^72 + x^71 + 2*x^69 + 2*x^66 + 2*x^65 + 2*x^64 + x^63 + 2*x^61 + 2*x^60 + x^59 + x^58 + x^55 + x^54 + 2*x^53 + x^52 + x^51 + x^50 + x^47 + x^46 + x^45 + x^44 + x^43 + x^42 + x^41 + x^40 + 2*x^39 + 2*x^38 + x^37 + x^36 + 2*x^35 + 2*x^34 + x^33 + x^32 + 2*x^30 + x^28 + 2*x^25 + x^22 + x^21 + x^20 + 2*x^19 + x^16 + x^13 + x^11 + x^10 + 2*x^8 + x^7 + x^6 + 2*x^5 + x^3 [7]: [177, 11, 102] Linear Code over GF(3) ConstructionXX using [6] [5] [4] [3] and [1] last modified: 2007-07-30
Lb(177,11) = 101 is found by shortening of: Lb(178,12) = 101 is found by truncation of: Lb(182,12) = 105 ARS Ub(177,11) = 111 follows by a one-step Griesmer bound from: Ub(65,10) = 37 follows by a one-step Griesmer bound from: Ub(27,9) = 12 is found by construction B: [consider deleting the (at most) 6 coordinates of a word in the dual]
Notes
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