lower bound: | 36 |
upper bound: | 36 |
Construction of a linear code [52,5,36] over GF(4): [1]: [1, 1, 1] Cyclic Linear Code over GF(2^2) RepetitionCode of length 1 [2]: [51, 5, 35] Cyclic Linear Code over GF(2^2) CyclicCode of length 51 with generating polynomial x^46 + w^2*x^45 + w*x^44 + w^2*x^42 + w^2*x^41 + w*x^39 + w*x^38 + w^2*x^37 + w*x^36 + w^2*x^35 + w^2*x^33 + w^2*x^32 + w^2*x^31 + w^2*x^30 + x^29 + w*x^28 + w^2*x^26 + w*x^25 + w*x^24 + w^2*x^23 + w*x^20 + w*x^18 + w^2*x^17 + w*x^16 + w*x^15 + w*x^14 + w*x^13 + x^12 + w^2*x^10 + w*x^9 + w*x^6 + w^2*x^5 + w^2*x^4 + w^2*x^2 + w [3]: [52, 5, 36] Linear Code over GF(2^2) ExtendCode [2] by 1 [4]: [51, 6, 34] Cyclic Linear Code over GF(2^2) CyclicCode of length 51 with generating polynomial x^45 + x^44 + w^2*x^41 + w*x^40 + w^2*x^39 + w^2*x^38 + w^2*x^37 + w*x^36 + x^35 + x^34 + w*x^33 + w^2*x^31 + w*x^30 + x^28 + w^2*x^25 + w^2*x^24 + w^2*x^23 + w*x^22 + w^2*x^21 + x^20 + w*x^17 + w*x^15 + x^14 + w*x^12 + w*x^11 + w^2*x^10 + w*x^9 + x^8 + w*x^7 + w^2*x^6 + w^2*x^5 + w*x^4 + w^2*x + 1 [5]: [52, 6, 35] Linear Code over GF(2^2) ExtendCode [4] by 1 [6]: [53, 6, 36] Linear Code over GF(2^2) ConstructionX using [5] [3] and [1] [7]: [52, 5, 36] Linear Code over GF(2^2) Shortening of [6] at { 53 } last modified: 2001-12-17
Lb(52,5) = 36 is found by shortening of: Lb(53,6) = 36 XX Ub(52,5) = 36 is found by considering shortening to: Ub(51,4) = 36 LMH
XX:
Notes
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