To meet the increasing demands for remote sensing, a number of radar systems using Linear Frequency Modulation (LFM) waveforms have been deployed, causing the problem of depleting frequency resources. To address this problem, several researchers have proposed the Spectrum Shared Radar System (SSRS) in which multiple radars share the same frequency band to transmit and receive their own signals. To mitigate the interferences caused by the signal transmission by other radars, SSRS employs orthogonal waveforms that inherit the orthogonality of the waveforms from orthogonal codes. However, the inherited orthogonality of the codes is significantly reduced when incorporating LFM waveforms with the codes. To solve this problem, in this paper, we propose a novel but simple scheme for generating a set of optimized coded LFM waveforms via new optimization framework. In the optimization framework, we minimize the weighted sum of autocorrelation sidelobe peaks () and cross-correlation peaks () of the coded LFM waveforms to maximize the orthogonality of the waveforms. Through computer simulations, we show that the waveforms generated by the proposed scheme outperform the waveforms created by previous proposals in terms of and .