This paper presents a method for improving the performance of logical algorithms in quantum computing by using correlated decoding of logical qubits during transversal entangling gates. The approach leverages the deterministic error propagation characteristics of transversal gates to enhance the accuracy of error correction. The study explores two decoding strategies: one that is highly accurate but computationally intensive, and another that is more efficient but less precise. The results show that correlated decoding significantly improves the performance of both Clifford and non-Clifford transversal entangling gates, reducing the number of rounds of noisy syndrome extraction required per gate and thus lowering the space-time cost of logical algorithms. The paper discusses the importance of quantum error correction in achieving scalable quantum computation and highlights recent experimental advances in manipulating logical qubits using transversal gates. It also addresses the challenges of implementing large-scale algorithms with protected logical qubits due to significant space-time overhead. The study demonstrates that correlated decoding can be applied to both Clifford and non-Clifford gates, with particular emphasis on the benefits of using correlated decoding in deep logical Clifford circuits. The results indicate that correlated decoding can reduce the space-time cost of large-scale logical algorithms and improve the threshold for fault-tolerant computation. The paper also explores the application of correlated decoding to non-Clifford gates, showing that it can significantly improve the logical error rate in certain scenarios. The study concludes that correlated decoding is a powerful tool for improving the performance of logical algorithms, and that it has the potential to reduce the space-time cost of large-scale quantum algorithms. The results are supported by numerical simulations and theoretical analysis, demonstrating the effectiveness of correlated decoding in enhancing the accuracy and efficiency of quantum error correction in logical circuits.This paper presents a method for improving the performance of logical algorithms in quantum computing by using correlated decoding of logical qubits during transversal entangling gates. The approach leverages the deterministic error propagation characteristics of transversal gates to enhance the accuracy of error correction. The study explores two decoding strategies: one that is highly accurate but computationally intensive, and another that is more efficient but less precise. The results show that correlated decoding significantly improves the performance of both Clifford and non-Clifford transversal entangling gates, reducing the number of rounds of noisy syndrome extraction required per gate and thus lowering the space-time cost of logical algorithms. The paper discusses the importance of quantum error correction in achieving scalable quantum computation and highlights recent experimental advances in manipulating logical qubits using transversal gates. It also addresses the challenges of implementing large-scale algorithms with protected logical qubits due to significant space-time overhead. The study demonstrates that correlated decoding can be applied to both Clifford and non-Clifford gates, with particular emphasis on the benefits of using correlated decoding in deep logical Clifford circuits. The results indicate that correlated decoding can reduce the space-time cost of large-scale logical algorithms and improve the threshold for fault-tolerant computation. The paper also explores the application of correlated decoding to non-Clifford gates, showing that it can significantly improve the logical error rate in certain scenarios. The study concludes that correlated decoding is a powerful tool for improving the performance of logical algorithms, and that it has the potential to reduce the space-time cost of large-scale quantum algorithms. The results are supported by numerical simulations and theoretical analysis, demonstrating the effectiveness of correlated decoding in enhancing the accuracy and efficiency of quantum error correction in logical circuits.