lower bound: | 57 |
upper bound: | 64 |
Construction of a linear code [108,12,57] over GF(3): [1]: Curve A Curve over GF(9): x[1]^105 + w^5*x[1]^102*x[3]^3 + x[1]^99*x[3]^6 + w^6*x[1]^96*x[3]^9 + x[1]^90*x[3]^15 + w^5*x[1]^87*x[2]*x[3]^17 + w^2*x[1]^87*x[3]^18 + w^2*x[1]^84*x[2]*x[3]^20 + w^5*x[1]^84*x[3]^21 + w^2*x[1]^81*x[3]^24 + w^2*x[1]^78*x[3]^27 + w^2*x[1]^75*x[2]^2*x[3]^28 + w^7*x[1]^75*x[3]^30 + w^2*x[1]^72*x[2]^2*x[3]^31 + w^2*x[1]^72*x[3]^33 + w*x[1]^69*x[2]^2*x[3]^34 + x[1]^69*x[3]^36 + w^2*x[1]^66*x[2]^2*x[3]^37 + w*x[1]^63*x[2]^2*x[3]^40 + w^2*x[1]^63*x[3]^42 + w^6*x[1]^60*x[2]^3*x[3]^42 + w^5*x[1]^60*x[2]^2*x[3]^43 + w^7*x[1]^60*x[2]*x[3]^44 + 2*x[1]^60*x[3]^45 + 2*x[1]^57*x[2]*x[3]^47 + w^7*x[1]^57*x[3]^48 + x[1]^54*x[2]^3*x[3]^48 + w*x[1]^54*x[2]^2*x[3]^49 + 2*x[1]^54*x[3]^51 + x[1]^51*x[2]^3*x[3]^51 + w*x[1]^51*x[2]^2*x[3]^52 + w*x[1]^51*x[3]^54 + w^3*x[1]^45*x[2]^4*x[3]^56 + w^6*x[1]^48*x[3]^57 + w^2*x[1]^45*x[2]^3*x[3]^57 + w^7*x[1]^45*x[2]^2*x[3]^58 + w*x[1]^42*x[2]^4*x[3]^59 + w*x[1]^45*x[3]^60 + x[1]^42*x[2]^3*x[3]^60 + w^6*x[1]^42*x[2]^2*x[3]^61 + w*x[1]^39*x[2]^4*x[3]^62 + w^7*x[1]^42*x[3]^63 + x[1]^39*x[2]^2*x[3]^64 + w*x[1]^36*x[2]^4*x[3]^65 + w^2*x[1]^36*x[2]^3*x[3]^66 + w^3*x[1]^36*x[2]^2*x[3]^67 + w*x[1]^36*x[3]^69 + w*x[1]^33*x[2]^2*x[3]^70 + w^6*x[1]^33*x[2]*x[3]^71 + w^3*x[1]^30*x[2]^4*x[3]^71 + w^3*x[1]^33*x[3]^72 + x[1]^30*x[2]^2*x[3]^73 + w^3*x[1]^30*x[2]*x[3]^74 + 2*x[1]^27*x[2]^4*x[3]^74 + w^6*x[1]^30*x[3]^75 + w^7*x[1]^24*x[2]^4*x[3]^77 + w^3*x[1]^27*x[3]^78 + w^6*x[1]^24*x[2]^3*x[3]^78 + w^6*x[1]^24*x[2]^2*x[3]^79 + w^6*x[1]^21*x[2]^4*x[3]^80 + w^7*x[1]^24*x[3]^81 + w^2*x[1]^21*x[2]^2*x[3]^82 + w*x[1]^18*x[2]^4*x[3]^83 + 2*x[1]^21*x[3]^84 + x[1]^18*x[2]^3*x[3]^84 + w^2*x[1]^15*x[2]^4*x[3]^86 + w^7*x[1]^18*x[3]^87 + w^2*x[1]^15*x[2]^3*x[3]^87 + w^6*x[1]^15*x[2]^2*x[3]^88 + w^5*x[1]^15*x[3]^90 + w^6*x[1]^12*x[2]^2*x[3]^91 + 2*x[1]^9*x[2]^4*x[3]^92 + 2*x[1]^9*x[2]^3*x[3]^93 + w^5*x[1]^9*x[2]^2*x[3]^94 + x[1]^6*x[2]^4*x[3]^95 + w^7*x[1]^9*x[3]^96 + x[1]^6*x[2]^3*x[3]^96 + w^6*x[1]^6*x[2]^2*x[3]^97 + 2*x[1]^6*x[2]*x[3]^98 + 2*x[1]^3*x[2]^4*x[3]^98 + w^6*x[2]^7*x[3]^98 + w*x[1]^6*x[3]^99 + w^5*x[1]^3*x[2]^2*x[3]^100 + w*x[1]^3*x[2]*x[3]^101 + w^6*x[2]^4*x[3]^101 + 2*x[1]^3*x[3]^102 + w^2*x[2]^3*x[3]^102 + w*x[2]^2*x[3]^103 + w*x[3]^105 where w := GF(9).1 [2]: [27, 6, 19] Linear Code over GF(3^2) AlgebraicGeometricCode from the curve [1] which is based on 1 divisors of degree [ 1 ] [3]: [121, 116, 3] "Hamming code (r = 5)" Linear Code over GF(3) 5-th order HammingCode over GF( 3) [4]: [121, 5, 81] Cyclic Linear Code over GF(3) Dual of [3] [5]: [119, 5, 79] Linear Code over GF(3) Puncturing of [4] at { 120 .. 121 } [6]: [40, 4, 27] Linear Code over GF(3) ResidueCode of [5] [7]: [38, 4, 25] Linear Code over GF(3) Puncturing of [6] at { 39 .. 40 } [8]: [13, 3, 9] Linear Code over GF(3) ResidueCode of [7] [9]: [11, 3, 7] Linear Code over GF(3) Puncturing of [8] at { 12 .. 13 } [10]: [4, 2, 3] Linear Code over GF(3) ResidueCode of [9] [11]: [108, 12, 57] Linear Code over GF(3) ZinovievCode using inner codes: [10], outer codes: [2] last modified: 2003-10-07
Lb(108,12) = 57 BZ Ub(108,12) = 64 is found by considering shortening to: Ub(107,11) = 64 BKn
BZ: E. L. Blokh & V. V. Zyablov, Coding of generalized concatenated codes, Probl. Inform. Transm. 10 (1974) 218-222.
Notes
|