lower bound: | 94 |
upper bound: | 97 |
Construction of a linear code [136,7,94] over GF(4): [1]: [12, 6, 6] Linear Code over GF(2^2) Extend the QRCode over GF(4)of length 11 [2]: [9, 3, 6] Linear Code over GF(2^2) Shortening of [1] at { 10 .. 12 } [3]: [126, 4, 94] Quasicyclic of degree 2 Linear Code over GF(2^2) QuasiCyclicCode of length 126 with generating polynomials: x^62 + w^2*x^61 + w*x^59 + w^2*x^58 + x^57 + w*x^56 + w^2*x^54 + w^2*x^53 + x^52 + w^2*x^51 + w^2*x^50 + w*x^49 + w*x^48 + w^2*x^47 + w^2*x^46 + w^2*x^45 + w*x^44 + x^43 + x^41 + w^2*x^40 + w^2*x^39 + w^2*x^38 + w^2*x^37 + w^2*x^35 + x^34 + x^33 + w*x^31 + x^30 + w*x^27 + w^2*x^25 + x^24 + w^2*x^23 + w*x^22 + w^2*x^21 + x^20 + w^2*x^19 + x^18 + w^2*x^16 + w^2*x^15 + w*x^13 + w*x^11 + w*x^8 + x^7 + w*x^6 + w*x^5 + w^2*x^4 + 1, x^61 + w^2*x^60 + w^2*x^59 + w^2*x^58 + w^2*x^57 + w^2*x^55 + x^54 + x^53 + w*x^51 + x^50 + w*x^47 + w^2*x^45 + x^44 + w^2*x^43 + w*x^42 + w^2*x^41 + x^40 + w^2*x^39 + x^38 + w^2*x^36 + w^2*x^35 + w*x^33 + w*x^31 + w*x^28 + x^27 + w*x^26 + w*x^25 + w^2*x^24 + x^20 + x^19 + w^2*x^18 + w*x^16 + w^2*x^15 + x^14 + w*x^13 + w^2*x^11 + w^2*x^10 + x^9 + w^2*x^8 + w^2*x^7 + w*x^6 + w*x^5 + w^2*x^4 + w^2*x^3 + w^2*x^2 + w*x + 1 [4]: [126, 7, 88] Quasicyclic of degree 2 Linear Code over GF(2^2) QuasiCyclicCode of length 126 with generating polynomials: w^2*x^62 + w^2*x^60 + w*x^59 + x^58 + x^57 + x^56 + w*x^55 + w*x^53 + x^52 + w*x^51 + x^50 + x^49 + x^48 + x^47 + x^46 + x^45 + x^43 + w^2*x^41 + w*x^39 + x^38 + w*x^37 + w*x^36 + x^35 + w^2*x^34 + x^33 + x^32 + w^2*x^31 + w^2*x^29 + w^2*x^27 + w*x^25 + w^2*x^24 + x^23 + w*x^22 + w^2*x^21 + x^20 + w^2*x^19 + w^2*x^18 + w*x^17 + x^15 + x^14 + w*x^13 + w^2*x^12 + w*x^11 + x^10 + w^2*x^8 + w*x^7 + 1, x^61 + w^2*x^60 + w*x^57 + w^2*x^56 + x^55 + x^54 + x^50 + w*x^49 + x^48 + x^47 + w^2*x^46 + w*x^45 + x^44 + w^2*x^43 + w*x^42 + w^2*x^41 + w*x^40 + w*x^39 + w^2*x^35 + x^34 + x^33 + x^32 + w*x^29 + x^28 + w^2*x^26 + x^25 + w^2*x^23 + w^2*x^22 + x^20 + w*x^19 + w*x^18 + w*x^17 + x^16 + x^15 + w*x^14 + x^13 + w^2*x^12 + w^2*x^11 + x^10 + w^2*x^9 + x^8 + w*x^7 + w*x^6 + w^2*x^4 + x^3 + x + 1 [5]: [135, 7, 94] Linear Code over GF(2^2) ConstructionX using [4] [3] and [2] [6]: [136, 7, 94] Linear Code over GF(2^2) ExtendCode [5] by 1 last modified: 2003-03-31
Lb(136,7) = 94 is found by lengthening of: Lb(135,7) = 94 GW2 Ub(136,7) = 97 DM3
GW2: M. Grassl & G. White, New Codes from Chains of Quasi-cyclic Codes, ISIT 2005.
Notes
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