lower bound: | 124 |
upper bound: | 127 |
Construction of a linear code [176,7,124] over GF(4): [1]: [1, 1, 1] Cyclic Linear Code over GF(2^2) RepetitionCode of length 1 [2]: [175, 6, 124] Quasicyclic of degree 5 Linear Code over GF(2^2) QuasiCyclicCode of length 175 with generating polynomials: x^34 + x^33 + w*x^31 + w*x^30 + w*x^29 + x^28 + x^27 + w^2*x^26 + x^24 + x^23 + w^2*x^21 + w*x^20 + w^2*x^19 + x^17 + x^16 + w*x^15 + w^2*x^14 + x^12 + w*x^10 + w*x^9 + x^8 + x^7 + w*x^6 + x, w^2*x^34 + x^32 + x^31 + w^2*x^30 + w*x^29 + w^2*x^28 + w*x^27 + w*x^26 + w^2*x^25 + w^2*x^24 + w^2*x^22 + w^2*x^21 + w*x^20 + x^19 + w^2*x^18 + w^2*x^17 + w^2*x^16 + x^14 + w^2*x^13 + x^12 + x^11 + x^10 + w*x^9 + w^2*x^8 + w*x^5 + w*x^2 + w*x + 1, x^34 + w*x^33 + w*x^32 + x^31 + x^30 + w*x^29 + x^28 + w*x^27 + w*x^26 + w*x^25 + w*x^24 + w^2*x^23 + w*x^22 + w*x^21 + w^2*x^19 + w^2*x^18 + w^2*x^16 + w^2*x^15 + w*x^13 + w*x^10 + x^9 + w*x^7 + x^6 + w^2*x^5 + w^2*x^4 + x^3 + w^2*x + 1, w*x^34 + w*x^33 + x^31 + w^2*x^30 + w^2*x^29 + w^2*x^28 + x^27 + x^26 + w*x^25 + x^23 + w^2*x^22 + x^20 + x^19 + x^18 + x^17 + x^15 + w^2*x^14 + w*x^13 + w*x^12 + x^11 + w^2*x^10 + x^9 + w*x^7 + w*x^4 + w^2*x^3 + w^2*x^2 + x + w, x^33 + w*x^32 + x^31 + w^2*x^29 + w^2*x^28 + w^2*x^26 + x^24 + w^2*x^23 + x^22 + w*x^21 + w^2*x^19 + w*x^18 + w*x^17 + w*x^16 + w*x^14 + x^12 + x^11 + w*x^9 + x^8 + w^2*x^7 + x^4 + w*x^3 + w^2*x^2 + w^2*x [3]: [175, 7, 123] Quasicyclic of degree 5 Linear Code over GF(2^2) QuasiCyclicCode of length 175 with generating polynomials: w^2*x^34 + x^33 + w^2*x^32 + w^2*x^30 + w^2*x^28 + w^2*x^27 + w*x^26 + w^2*x^25 + x^24 + w^2*x^23 + x^22 + w*x^21 + x^19 + w*x^17 + w*x^15 + w^2*x^14 + w*x^13 + w*x^11 + x^10 + w*x^9 + x^8 + x^7 + 1, w^2*x^34 + w^2*x^33 + w^2*x^32 + w*x^31 + x^30 + w^2*x^29 + w*x^28 + w^2*x^27 + w^2*x^26 + x^25 + x^24 + w*x^23 + w^2*x^22 + w*x^21 + w^2*x^20 + w^2*x^19 + w*x^18 + w^2*x^17 + w*x^16 + w^2*x^15 + x^14 + w^2*x^13 + w^2*x^12 + w*x^11 + x^10 + x^9 + w^2*x^8 + w^2*x^7 + w^2*x^6 + w^2*x^5 + x^4 + w*x^3 + w^2*x^2 + w^2*x + 1, x^34 + x^33 + w^2*x^32 + w*x^31 + x^30 + x^29 + w^2*x^28 + x^27 + w*x^24 + w^2*x^23 + w*x^22 + w*x^21 + w^2*x^19 + x^18 + x^17 + x^16 + w*x^15 + w^2*x^13 + x^11 + w^2*x^10 + w*x^9 + x^8 + x^5 + x^3 + w*x^2 + w^2*x + w, x^34 + x^30 + x^28 + w^2*x^26 + w^2*x^25 + x^24 + w*x^23 + w*x^22 + x^21 + w^2*x^19 + w^2*x^18 + w*x^17 + x^16 + w^2*x^14 + x^13 + x^10 + w^2*x^8 + w*x^7 + w*x^6 + w*x^5 + w*x^4 + w^2*x + w^2, w*x^34 + w^2*x^33 + w^2*x^31 + w^2*x^30 + w^2*x^29 + w*x^27 + x^26 + w^2*x^25 + w^2*x^22 + w^2*x^21 + x^20 + w*x^19 + x^17 + x^16 + w^2*x^15 + w^2*x^13 + w*x^12 + x^11 + x^10 + x^9 + w^2*x^8 + x^7 + x^6 + x^5 + x^4 + w^2*x + 1 [4]: [176, 7, 124] Linear Code over GF(2^2) ConstructionX using [3] [2] and [1] last modified: 2008-06-13
Lb(176,7) = 121 is found by truncation of: Lb(183,7) = 128 GW2 Ub(176,7) = 127 DM3
GW2: M. Grassl & G. White, New Codes from Chains of Quasi-cyclic Codes, ISIT 2005.
Notes
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