## 1 Introduction  
Secret sharing is a branch of cryptography [1], in which the dealer distributes a secret to all participants and only legitimate participants can reconstruct the shared secret in the cooperation fashion. The dealer distributes a secret message \(s\) to \(n\) participants which at least \(t\leq n\) participants combine to recover the secret. It is known as a \((t,n)\)-threshold scheme [2; 3; 4; 5; 6; 7; 8; 9]. Quantum secret sharing (QSS) is an extension of classical secret sharing via quantum states. Compared with the classical secret sharing, QSS protocols can achieve unconditional security based on the quantum no-cloning theorem and the Heisenberg uncertainty principle [10]. Quantum secret sharing (QSS) can be categorized into discrete variable QSS (DVQSS) [11; 12; 13; 14] and continuous variable QSS (CVQSS) [15; 16; 17; 18; 19; 20; 21; 22] based on the carriers used. In DVQSS, the discrete variable quantum states are used for the secret sharing, in which it carries information via weak laser pulses or the single photons. Owing to the low channel capacity and the difficulty of the preparation of single photons, it is difficult to implement in practices. In order to avoid these shortages, the continuous variable quantum states, such as coherent states and squeezed states, can be used for the information carriers, resulting in the CVQSS. Coherent states can be generated and operated by linear optical components and squeezed states can be generated from them through non-linear interactions. Furthermore, both of them increase the channel capacity. In the traditional QSS schemes, most of them are \((n,n)\)-threshold schemes, in which only all the \(n\) participants work together can recover the secret message from dealer, but any part of participants are impossible to restore the secret. For example, [PERSON] et al. proposed an initial \((t,n)\) threshold DVQSS protocol in theoretics [11]. Correspondingly, the CVQSS was proposed with its interferometric realization that depends on infinite squeezing [23]. After that, the (2,3) threshold scheme was designed using entangled system [16]. Thereafter, the \((n,n)\)-threshold protocol was dished with weak coherent state [24]. However, most of QSS protocols are based on squeezed states which are difficult to prepare in the laboratory, compared with coherent states. Moreover, all participants have equal ability to recover the initial secret from the dealer in traditional \((t,n)\) threshold schemes. They cannot satisfy the practical conditions which needs some specifically designated participants to share message and accomplish tasks in a large group. Currently, the Gaussian modulated coherent state (GMCS) has been elegantly applied in continuous variable quantum cryptography [25; 26; 27]. The Gaussian modulation encodes the key information by modulating the quadratures the amplitude \(X\) and the phase \(P\) of few-photon coherent states with a centered Gaussian distribution, where \(X\) and \(P\) quadratures can be measured by a heterodyne detector or homodyne detector [28; 29; 30; 31]. The GMCS-involved scheme has been proved to be secure against collective attacks and coherent attacks. Motivated by the elegant characteristics of the GMCS-involved system, we suggest an approach for establishing the GMCS-based CVQSS system. An improved \((t,n)\) threshold scheme will be proposed with weak coherent states. The main feature is that, instead of all participants have equal ability to recover the secret, it requires specially designated participants for the secret sharing. Each participant imports the locally prepared GMCS into a circulating optical mode with a beam splitter, which can be implemented with current optical technologies. Compared with modulating quantum state of the passing-through photon, this can make our protocol flexible and avoid obstruction from the eavesdroppers in the quantum state preparation. The paper is organized as follows. In Section 2, we present the GMCS-involved \((t,n)\) scheme for the CVQSS system.