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Traditional functional linked neural networks (FLNNs) impose a significant computational burden due to their input expansion, primarily stemming from the utilization of digital filters. This paper presents a Laguerre FLNNs filter for nonlinear active noise control (NANC) systems. By employing the truncated Laguerre series, the presented filter achieves effective approximation of long primary paths with a reduced filter length. Moreover, we develop adaptive algorithms rooted in information-theoretic learning (ITL) within the framework of the Laguerre-FLNNs NANC model. Using the ITL criterions, a Laguerre filtered-s maximum correntropy criterion (LFsMCC) algorithm is derived and a Laguerre filtered-s quantized minimum error entropy criterion (LFsQMEE) algorithm is proposed by minimizing Renyi's quadratic entropy. To reduce the computation cost, an online vector quantization method is utilized to improve the LFsQMEE. This technique selectively quantizes the error vectors, reducing them to a smaller subset of samples within the codebook. Moreover, an enhanced LFsQMEE with a fiducial point is introduced. The steady-state performance and the computational complexity are analyzed. Theoretical analysis is validated through simulations and the control performance of the proposed model and algorithms is tested in experiments with both simulated and real paths. [ABSTRACT FROM AUTHOR]