lower bound: | 26 |
upper bound: | 27 |
Construction of a linear code [35,5,26] over GF(7): [1]: Curve A Curve over GF(7): x[1]^9*x[2]^3 + 3*x[1]^8*x[2]^4 + 3*x[1]^7*x[2]^5 + x[1]^6*x[2]^6 + 4*x[1]^9*x[2]^2*x[3] + 5*x[1]^8*x[2]^3*x[3] + x[1]^6*x[2]^5*x[3] + 2*x[1]^5*x[2]^6*x[3] + 3*x[1]^9*x[2]*x[3]^2 + 2*x[1]^8*x[2]^2*x[3]^2 + 2*x[1]^7*x[2]^3*x[3]^2 + x[1]^6*x[2]^4*x[3]^2 + 2*x[1]^5*x[2]^5*x[3]^2 + 4*x[1]^4*x[2]^6*x[3]^2 + 3*x[1]^8*x[2]*x[3]^3 + 6*x[1]^7*x[2]^2*x[3]^3 + 4*x[1]^6*x[2]^3*x[3]^3 + 2*x[1]^4*x[2]^5*x[3]^3 + x[1]^3*x[2]^6*x[3]^3 + 4*x[1]^8*x[3]^4 + 4*x[1]^7*x[2]*x[3]^4 + 6*x[1]^6*x[2]^2*x[3]^4 + 2*x[1]^5*x[2]^3*x[3]^4 + 6*x[1]^4*x[2]^4*x[3]^4 + 3*x[1]^3*x[2]^5*x[3]^4 + 2*x[1]^2*x[2]^6*x[3]^4 + 3*x[1]^7*x[3]^5 + 3*x[1]^6*x[2]*x[3]^5 + 2*x[1]^3*x[2]^4*x[3]^5 + 3*x[1]^2*x[2]^5*x[3]^5 + 4*x[1]*x[2]^6*x[3]^5 + 3*x[1]^6*x[3]^6 + 5*x[1]^5*x[2]*x[3]^6 + 2*x[1]^4*x[2]^2*x[3]^6 + 2*x[1]^3*x[2]^3*x[3]^6 + 6*x[1]^2*x[2]^4*x[3]^6 + 5*x[1]*x[2]^5*x[3]^6 + x[2]^6*x[3]^6 + 6*x[1]^5*x[3]^7 + x[1]^3*x[2]^2*x[3]^7 + 2*x[1]^2*x[2]^3*x[3]^7 + 3*x[1]*x[2]^4*x[3]^7 + 5*x[2]^5*x[3]^7 + 6*x[1]^4*x[3]^8 + 2*x[1]^3*x[2]*x[3]^8 + 2*x[1]*x[2]^3*x[3]^8 + 6*x[2]^4*x[3]^8 + 2*x[1]^3*x[3]^9 + x[1]^2*x[2]*x[3]^9 + 6*x[1]*x[2]^2*x[3]^9 + 6*x[2]^3*x[3]^9 + 2*x[1]^2*x[3]^10 + 3*x[1]*x[2]*x[3]^10 + 6*x[2]^2*x[3]^10 + 3*x[1]*x[3]^11 + x[2]*x[3]^11 + 6*x[3]^12 [2]: [35, 5, 26] Linear Code over GF(7) AlgebraicGeometricCode from the curve [1] which is based on 1 divisors of degree [ 1 ] last modified: 2003-06-24
Lb(35,5) = 25 is found by shortening of: Lb(36,6) = 25 is found by truncation of: Lb(38,6) = 27 DaH Ub(35,5) = 27 is found by considering shortening to: Ub(33,3) = 27 is found by considering truncation to: Ub(30,3) = 24 Hi4
Hi4: R. Hill, Optimal linear codes, pp. 75-104 in: Cryptography and Coding II (C. Mitchell, ed.), Oxford Univ. Press, 1992.
Notes
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