Bounds on the minimum distance of linear codes

Bounds on linear codes [42,10] over GF(3)

Construction

Construction of a linear code [42,10,21] over GF(3):
[1]:  [1, 1, 1] Cyclic Linear Code over GF(3)
     RepetitionCode of length 1
[2]:  [40, 9, 20] Quasicyclic of degree 4 Linear Code over GF(3)
     QuasiCyclicCode of length 40 with generating polynomials: 2*x^8 + x^6,  2*x^9 + x^8 + x^6 + 2*x^5 + x^4 + x^3 + x^2 + 2*x,  x^9 + 2*x^8 + x^6 + x^5 + x^3 + x^2 + x,  x^9 + 2*x^8 + x^7 + 2*x^6 + x^5 + x^4 + 2*x^3 + x^2 + x
[3]:  [40, 9, 20] Quasicyclic of degree 4 Linear Code over GF(3)
     QuasiCyclicCode of length 40 with generating polynomials: 2*x^9 + x^2,  x^9 + x^8 + x^7 + 2*x^6 + 2*x^3 + x^2 + 2*x + 2,  x^8 + x^6 + 2*x^5 + 2*x^4 + 2*x^3 + x^2 + 2*x + 1,  2*x^8 + 2*x^6 + x^4 + 2*x + 2
[4]:  [40, 10, 19] Quasicyclic of degree 4 Linear Code over GF(3)
     QuasiCyclicCode of length 40 with generating polynomials: 2*x^9 + x^2,  2*x^9 + 2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2,  x^9 + 2*x^8 + x^7 + 2*x^6 + 2*x^2 + 2,  2*x^8 + 2*x^6 + x^4 + 2*x + 2
[5]:  [42, 10, 21] Linear Code over GF(3)
     ConstructionXX using [4] [3] [2] [1] and [1]

last modified: 2005-12-02

From Brouwer's table (as of 2007-02-13)

Lb(42,10) = 20 is found by shortening of:
Lb(43,11) = 20 is found by truncation of:
Lb(44,11) = 21 DaH

Ub(42,10) = 22 follows by a one-step Griesmer bound from:
Ub(19,9) = 7 is found by considering shortening to:
Ub(16,6) = 7 vE2

References