lower bound: | 28 |
upper bound: | 42 |
Construction of a linear code [98,40,28] over GF(4): [1]: [2, 2, 1] Cyclic Linear Code over GF(2^2) UniverseCode of length 2 [2]: [96, 38, 28] Quasicyclic of degree 2 Linear Code over GF(2^2) QuasiCyclicCode of length 96 with generating polynomials: x^44 + x^42 + x^38 + 1, x^47 + w*x^46 + w^2*x^44 + w^2*x^43 + w*x^42 + w^2*x^41 + x^40 + w^2*x^36 + x^33 + x^32 + w^2*x^31 + w^2*x^30 + w*x^29 + x^26 + x^25 + x^24 + w*x^23 + w*x^22 + w^2*x^21 + x^20 + x^19 + w^2*x^17 + w*x^16 + w^2*x^15 + w^2*x^14 + x^12 + x^11 + x^10 + w^2*x^9 + x^8 + w*x^7 + w*x^6 + w*x^4 + w*x^3 + w*x [3]: [96, 40, 27] Quasicyclic of degree 2 Linear Code over GF(2^2) QuasiCyclicCode of length 96 with generating polynomials: x^47 + x^43 + x^41 + x^25, w^2*x^47 + w*x^46 + w^2*x^44 + w^2*x^43 + x^42 + w^2*x^41 + x^40 + w*x^38 + w^2*x^37 + w^2*x^36 + w*x^35 + w^2*x^32 + w*x^31 + x^30 + x^26 + w^2*x^25 + w*x^22 + x^21 + x^20 + w^2*x^18 + w^2*x^17 + w^2*x^15 + w^2*x^14 + w*x^13 + w^2*x^12 + w*x^11 + w*x^10 + w^2*x^7 + w^2*x^5 + w^2*x^4 + w*x^3 + x^2 + w^2 [4]: [98, 40, 28] Linear Code over GF(2^2) ConstructionX using [3] [2] and [1] last modified: 2020-07-28
Lb(98,40) = 26 is found by taking a subcode of: Lb(98,41) = 26 is found by shortening of: Lb(100,43) = 26 Var Ub(98,40) = 42 is found by considering shortening to: Ub(88,30) = 42 LP
Var: From the Varshamov-Gilbert bound. Cf. R.R. Varshamov, Problems of the general theory of linear coding, Ph.D. thesis, Moscow State Univ., 1959. (Russian)
Notes
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