lower bound: | 100 |
upper bound: | 105 |
Construction of a linear code [148,8,100] over GF(4): [1]: [1, 1, 1] Cyclic Linear Code over GF(2^2) RepetitionCode of length 1 [2]: [147, 7, 100] Quasicyclic of degree 7 Linear Code over GF(2^2) QuasiCyclicCode of length 147 with generating polynomials: w^2*x^20 + w*x^18 + w*x^16 + w*x^15 + w*x^14 + w*x^13 + w^2*x^11 + w^2*x^9 + w^2*x^8 + w^2*x^7 + x^6, w^2*x^20 + x^19 + w*x^18 + w^2*x^17 + w^2*x^16 + x^14 + w*x^13 + w*x^12 + w^2*x^11 + w^2*x^10 + x^9 + w^2*x^8 + x^7 + x^6 + w^2*x^3 + x + 1, w*x^18 + x^17 + x^16 + x^15 + w*x^14 + w^2*x^13 + w^2*x^11 + x^9 + w*x^8 + x^6 + w^2*x^3 + x^2 + 1, w*x^19 + w*x^18 + w^2*x^17 + w^2*x^15 + x^14 + w^2*x^13 + w^2*x^12 + x^11 + w^2*x^10 + w*x^9 + w^2*x^8 + x^6 + w^2*x^4 + w^2*x^3 + w^2*x^2 + w^2*x + w^2, w*x^20 + w^2*x^18 + w*x^15 + x^14 + w*x^13 + w*x^12 + x^11 + x^10 + x^9 + w^2*x^8 + w^2*x^7 + w*x^6 + w^2*x^5 + w*x^3 + w*x^2 + w, w^2*x^20 + w^2*x^19 + x^17 + w*x^15 + w^2*x^13 + x^12 + w*x^11 + x^10 + x^9 + x^8 + w^2*x^7 + w^2*x^6 + w^2*x^4 + x^3 + w*x^2 + w^2*x + 1, x^20 + x^19 + w*x^17 + w*x^16 + w^2*x^15 + w^2*x^14 + x^13 + w*x^12 + w*x^11 + w*x^10 + w*x^9 + w^2*x^8 + w*x^7 + x^6 + w^2*x^4 + w*x^3 + w*x^2 + w^2*x + 1 [3]: [147, 8, 99] Quasicyclic of degree 7 Linear Code over GF(2^2) QuasiCyclicCode of length 147 with generating polynomials: w*x^20 + w^2*x^17 + w*x^16 + w^2*x^14 + x^13 + w^2*x^12 + x^11 + w^2*x^10 + x^8 + 1, w^2*x^19 + x^17 + w*x^16 + x^15 + x^14 + x^13 + w^2*x^12 + w*x^10 + w*x^9 + x^8 + x^4 + w*x^3 + x^2 + 1, x^20 + x^19 + w*x^17 + x^16 + x^15 + w^2*x^14 + x^13 + w^2*x^12 + x^11 + w^2*x^9 + x^8 + x^4 + w*x + w^2, x^20 + x^19 + w^2*x^18 + x^17 + w^2*x^16 + w^2*x^15 + x^13 + x^11 + x^10 + w^2*x^9 + x^8 + x^5 + w^2*x^4 + x^2 + w^2*x + 1, w*x^20 + w*x^19 + w^2*x^18 + x^17 + x^16 + w^2*x^14 + w*x^13 + x^12 + w*x^10 + w*x^9 + w*x^8 + x^6 + w*x^5 + w^2*x^3 + x^2 + x + 1, w*x^20 + w^2*x^19 + w^2*x^18 + x^17 + x^16 + w*x^15 + w*x^14 + x^13 + x^12 + w*x^10 + x^9 + w^2*x^8 + x^5 + w^2*x^3 + w*x + w, w^2*x^20 + x^19 + x^18 + x^17 + w^2*x^16 + w*x^14 + w^2*x^12 + w*x^11 + x^9 + x^8 + x^5 + x^4 + x^3 + w^2*x^2 + w^2*x + w^2 [4]: [148, 8, 100] Linear Code over GF(2^2) ConstructionX using [3] [2] and [1] last modified: 2008-06-16
Lb(148,8) = 98 is found by taking a subcode of: Lb(148,9) = 98 MTS Ub(148,8) = 105 Da1
MTS: Tatsuya Maruta, Mito Takenaka, Maori Shinohara & Yukie Shobara, Constructing new linear codes from pseudo-cyclic codes, pp. 292-298 in Proc. 9th International Workshop on Algebraic and Combinatorial Coding Theory(ACCT) in Kranevo, Bulgaria, 2004.
Notes
|