lower bound: | 66 |
upper bound: | 70 |
Construction of a linear code [152,13,66] over GF(2): [1]: [150, 13, 65] Quasicyclic of degree 10 Linear Code over GF(2) QuasiCyclicCode of length 150 stacked to height 2 with generating polynomials: x^14 + x^12 + x^8 + 1, x^14 + x^13 + x^12 + x^9 + x^8 + x^7 + x^6 + x^4 + x + 1, x^13 + x^11 + x^10 + x^6 + x^4 + x^2 + x + 1, x^14 + x^13 + x^10 + x^7 + x^6 + x^5 + x + 1, x^12 + x^9 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2, x^13 + x^9 + x^7 + x^6 + x^4 + x, x^7 + x^6 + x^4 + 1, x^14 + x^12 + x^11 + x^10 + x^8 + x^7 + x^5 + x^4 + x + 1, x^11 + x^9 + x^8 + x^6 + x^3 + 1, x^14 + x^13 + x^12 + x^11 + x^9 + x^6 + x^5 + x^4 + x^3 + x^2, x^13 + x^12 + x^11 + x^9 + x^8 + x^5 + x^3, x^13 + x^8 + x^7 + x^6 + x^4 + x^3 + 1, x^14 + x^12 + x^10 + x^9 + x^8 + x^7 + x^3 + 1, x^12 + x^10 + x^5 + x^4 + x^3 + x + 1, x^14 + x^13 + x^12 + x^11 + x^7 + x^4 + x^3 + x, x^14 + x^13 + x^12 + x^8 + x^5 + x^4 + x^2 + 1, x^14 + x^11 + x^10 + x^8 + x^6 + x^5 + x^4 + x^3, x^13 + x^8 + x^7 + x^6 + x^4 + x^3 + 1, x^13 + x^12 + x^11 + x^10 + x^6 + x^3 + x^2 + 1, x^14 + x^13 + x^11 + x^10 + x^7 + x^5 + 1 [2]: [151, 13, 66] Linear Code over GF(2) ExtendCode [1] by 1 [3]: [152, 13, 66] Linear Code over GF(2) ExtendCode [2] by 1 last modified: 2001-01-30
Lb(152,13) = 66 is found by adding a parity check bit to: Lb(151,13) = 65 GG Ub(152,13) = 70 follows by a one-step Griesmer bound from: Ub(81,12) = 35 is found by considering shortening to: Ub(80,11) = 35 is found by considering truncation to: Ub(79,11) = 34 Ja
Ja: D.B. Jaffe, Binary linear codes: new results on nonexistence, 1996, code.ps.gz.
Notes
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