lower bound: | 28 |
upper bound: | 41 |
Construction of a linear code [98,41,28] over GF(4): [1]: [2, 2, 1] Cyclic Linear Code over GF(2^2) UniverseCode of length 2 [2]: [96, 39, 28] Quasicyclic of degree 2 Linear Code over GF(2^2) QuasiCyclicCode of length 96 with generating polynomials: x^47 + x^45 + x^42 + x^41 + x^39 + x^6, x^47 + w*x^45 + w*x^44 + w*x^43 + x^42 + x^41 + x^39 + w*x^38 + w^2*x^37 + w*x^34 + x^32 + w*x^31 + w*x^30 + w*x^29 + x^27 + w^2*x^24 + x^22 + x^20 + x^18 + x^17 + w^2*x^13 + x^12 + x^11 + w^2*x^9 + w*x^8 + x^7 + x^6 + w*x^5 + w^2*x^4 + x^3 + w*x^2 + x + 1 [3]: [96, 41, 27] Quasicyclic of degree 2 Linear Code over GF(2^2) QuasiCyclicCode of length 96 with generating polynomials: x^46 + x^45 + x^42 + x, w*x^47 + w*x^46 + w^2*x^45 + w^2*x^43 + x^42 + w*x^41 + w^2*x^40 + x^39 + w^2*x^38 + w*x^36 + w^2*x^35 + w^2*x^33 + w*x^32 + w*x^31 + w*x^30 + w*x^28 + x^27 + w*x^26 + x^25 + x^24 + x^23 + w*x^22 + x^21 + w^2*x^16 + x^15 + w*x^14 + w^2*x^13 + w^2*x^12 + w^2*x^11 + w*x^10 + x^9 + w*x^8 + w*x^7 + w^2*x^6 + w^2*x^5 + w*x^4 + x^3 + x^2 + w^2*x [4]: [98, 41, 28] Linear Code over GF(2^2) ConstructionX using [3] [2] and [1] last modified: 2020-08-03
Lb(98,41) = 26 is found by shortening of: Lb(100,43) = 26 Var Ub(98,41) = 41 is found by considering shortening to: Ub(92,35) = 41 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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