lower bound: | 58 |
upper bound: | 64 |
Construction of a linear code [144,16,58] over GF(2): [1]: [3, 2, 2] Cyclic Linear Code over GF(2) CordaroWagnerCode of length 3 [2]: [51, 8, 32] Cyclic Linear Code over GF(2^2) CyclicCode of length 51 with generating polynomial x^43 + w^2*x^40 + x^38 + x^37 + x^36 + w*x^35 + x^34 + x^33 + w*x^32 + x^30 + w*x^29 + w*x^28 + w^2*x^26 + w*x^24 + x^22 + w^2*x^21 + x^20 + w*x^19 + w*x^18 + w*x^16 + w^2*x^15 + w*x^13 + w^2*x^12 + w^2*x^11 + w*x^9 + w^2*x^7 + w*x^6 + w*x^5 + w*x^4 + x^3 + w*x + w^2 [3]: [48, 8, 29] Linear Code over GF(2^2) Puncturing of [2] at { 49 .. 51 } [4]: [144, 16, 58] Linear Code over GF(2) ConcatenatedCode of [3] and [1] last modified: 2003-12-05
Lb(144,16) = 57 XB Ub(144,16) = 64 follows by a one-step Griesmer bound from: Ub(79,15) = 32 follows by a one-step Griesmer bound from: Ub(46,14) = 16 follows by a one-step Griesmer bound from: Ub(29,13) = 8 follows by a one-step Griesmer bound from: Ub(20,12) = 4 is found by considering shortening to: Ub(18,10) = 4 otherwise adding a parity check bit would contradict: Ub(19,10) = 5 is found by construction B: [consider deleting the (at most) 6 coordinates of a word in the dual]
Notes
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