The new upper bounds on the rate of linear k-hash codes have significant implications for the zero-error list-decoding capacity of certain discrete channels and the study of perfect hash functions. By establishing tighter upper bounds, researchers can gain a better understanding of the maximum achievable rates for linear k-hash codes, which directly impacts the efficiency and reliability of error-correction and data transmission systems. In the context of zero-error list-decoding capacity, the improved bounds provide insights into the optimal performance limits of coding schemes in scenarios where decoding errors are not tolerated. Additionally, in the study of perfect hash functions, the upper bounds offer valuable guidance on the design and implementation of efficient hashing algorithms with minimal collisions and maximum data retrieval efficiency. Overall, the implications of these new upper bounds extend to various applications in information theory, coding theory, and data storage systems, driving advancements in error-correction techniques and data processing algorithms.