lower bound: | 66 |
upper bound: | 70 |
Construction of a linear code [100,8,66] over GF(4): [1]: [102, 8, 68] Quasicyclic of degree 6 Linear Code over GF(2^2) QuasiCyclicCode of length 102 with generating polynomials: w*x^16 + w^2*x^14 + w^2*x^13 + w^2*x^12 + w^2*x^10 + w*x^9 + x^8 + x^3, w*x^16 + x^14 + w*x^13 + w*x^11 + w^2*x^8 + x^6 + x^4 + w^2*x^3 + w*x^2 + 1, x^16 + w*x^15 + w^2*x^14 + w^2*x^13 + w^2*x^12 + x^11 + w*x^10 + w*x^9 + w^2*x^8 + x^6 + x^5 + w^2*x^4 + w^2*x^3 + w*x^2 + w*x + w, w^2*x^15 + w*x^14 + w^2*x^9 + w*x^8 + w^2*x^6 + x^5 + w^2*x^3 + w*x^2 + x + w, w^2*x^16 + w^2*x^14 + w*x^13 + w^2*x^12 + w^2*x^10 + w*x^9 + x^8 + x^7 + x^4 + w^2*x^2 + w^2*x + 1, w^2*x^16 + x^14 + w^2*x^10 + w^2*x^9 + w^2*x^8 + x^7 + w^2*x^6 + w*x^5 + w*x^4 + w*x^2 + w^2*x + w [2]: [100, 8, 66] Linear Code over GF(2^2) Puncturing of [1] at { 101 .. 102 } last modified: 2008-06-16
Lb(100,8) = 64 is found by shortening of: Lb(102,10) = 64 DaH Ub(100,8) = 70 follows by a one-step Griesmer bound from: Ub(29,7) = 17 is found by considering shortening to: Ub(27,5) = 17 is found by considering truncation to: Ub(26,5) = 16 BGV
DaH: Rumen Daskalov & Plamen Hristov, New One-Generator Quasi-Cyclic Codes over GF(7), preprint, Oct 2001. R. Daskalov & P Hristov, New One-Generator Quasi-Twisted Codes over GF(5), (preprint) Oct. 2001. R. Daskalov & P Hristov, New Quasi-Twisted Degenerate Ternary Linear Codes, preprint, Nov 2001. Email, 2002-2003.
Notes
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