lower bound: | 48 |
upper bound: | 49 |
Construction of a linear code [112,14,48] over GF(2): [1]: [112, 14, 48] Quasicyclic of degree 8 Linear Code over GF(2) QuasiCyclicCode of length 112 stacked to height 2 with generating polynomials: x^10 + x^8 + x^6 + 1, x^12 + x^11 + x^9 + x^8 + x^7 + x^6 + x^4 + x, x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x + 1, x^13 + x^12 + x^11 + x^8 + x^6 + x^5 + x^4 + x, x^9 + x^8 + x^5 + x^4 + x^3 + x^2 + x + 1, x^13 + x^12 + x^10 + x^7 + x^4 + x^3 + x + 1, x^8 + x^4 + x^2 + 1, x^12 + x^11 + x^10 + x^7 + x^5 + x^4 + x^3 + 1, x^12 + x^10 + x^6, x^9 + x^7 + x^3, x^10 + x^7 + x^6 + x^5 + x^4 + x^2 + x, x^13 + x^11 + x^10 + x^9 + x^3 + x^2 + 1, x^10 + x^9 + x^5 + x^3 + x^2 + x + 1, x^13 + x^11 + x^10 + x^8 + x^7 + x^6 + 1, x^13 + x^11 + x^9 + x^7 + x^5 + x^3 + x, x^10 + x^9 + x^5 + x^3 + x^2 + x + 1 last modified: 2010-11-13
Lb(112,14) = 45 is found by construction A: taking the residue of: Lb(201,15) = 89 is found by truncation of: Lb(202,15) = 90 EB1 Ub(112,14) = 49 follows by a one-step Griesmer bound from: Ub(62,13) = 24 is found by considering shortening to: Ub(60,11) = 24 otherwise adding a parity check bit would contradict: Ub(61,11) = 25 is found by construction B: [consider deleting the (at most) 4 coordinates of a word in the dual]
Notes
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