lower bound: | 146 |
upper bound: | 150 |
Construction of a linear code [231,8,146] over GF(3): [1]: [121, 116, 3] "Hamming code (r = 5)" Linear Code over GF(3) 5-th order HammingCode over GF( 3) [2]: [121, 5, 81] Cyclic Linear Code over GF(3) Dual of [1] [3]: [119, 5, 79] Linear Code over GF(3) Puncturing of [2] at { 120 .. 121 } [4]: [40, 4, 27] Linear Code over GF(3) ResidueCode of [3] [5]: [38, 4, 25] Linear Code over GF(3) Puncturing of [4] at { 39 .. 40 } [6]: [13, 3, 9] Linear Code over GF(3) ResidueCode of [5] [7]: [11, 3, 7] Linear Code over GF(3) Puncturing of [6] at { 12 .. 13 } [8]: [4, 2, 3] Linear Code over GF(3) ResidueCode of [7] [9]: [82, 4, 72] Constacyclic by $.1 Linear Code over GF(3^2) ConstaCyclicCode generated by $.1^6*x^81 + 2*x^80 + $.1^6*x^79 + x^78 + 2*x^77 + $.1^6*x^76 + $.1^6*x^75 + $.1^6*x^73 + $.1^2*x^72 + x^71 + $.1^7*x^70 + $.1^2*x^68 + $.1^2*x^67 + $.1^2*x^66 + 2*x^65 + $.1^2*x^64 + $.1^3*x^63 + $.1^6*x^62 + $.1^2*x^60 + $.1^7*x^59 + 2*x^58 + $.1^2*x^57 + $.1^6*x^56 + $.1^5*x^55 + $.1*x^54 + $.1^2*x^53 + $.1^7*x^52 + x^51 + $.1^2*x^50 + $.1^3*x^49 + $.1*x^48 + $.1^6*x^47 + $.1^6*x^46 + 2*x^45 + $.1^2*x^44 + $.1^7*x^42 + $.1^2*x^41 + $.1^5*x^40 + $.1^6*x^39 + $.1^2*x^38 + $.1^5*x^37 + $.1^5*x^36 + 2*x^35 + 2*x^34 + x^33 + x^32 + $.1^5*x^31 + $.1^7*x^30 + 2*x^29 + $.1^7*x^28 + $.1^3*x^27 + $.1^7*x^26 + $.1^5*x^24 + $.1^3*x^23 + $.1^3*x^22 + $.1^6*x^21 + $.1^5*x^20 + $.1^6*x^19 + $.1^7*x^18 + $.1^6*x^16 + x^15 + $.1^3*x^14 + x^13 + $.1^2*x^11 + $.1^3*x^10 + $.1^2*x^9 + $.1^7*x^8 + $.1^6*x^7 + $.1^5*x^6 + x^5 + $.1^2*x^4 + 1 with shift constant $.1 [10]: [58, 4, 49] Linear Code over GF(3^2) Puncturing of [9] at { 1, 2, 3, 4, 5, 6, 7, 13, 20, 24, 25, 27, 30, 33, 34, 38, 39, 44, 47, 51, 57, 70, 76, 82 } [11]: [232, 8, 147] Linear Code over GF(3) ConcatenatedCode of [10] and [8] [12]: [231, 8, 146] Linear Code over GF(3) Puncturing of [11] at { 232 } last modified: 2003-11-04
Lb(231,8) = 144 is found by shortening of: Lb(234,11) = 144 is found by truncation of: Lb(243,11) = 153 XBC Ub(231,8) = 150 follows by a one-step Griesmer bound from: Ub(80,7) = 50 follows by a one-step Griesmer bound from: Ub(29,6) = 16 is found by considering truncation to: Ub(28,6) = 15 HHM
XBC: Extended BCH code.
Notes
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