AI编程能力边界探索：基于 Claude Code 的 Spec Coding 项目实战｜得物技术

Polarization-adjusted convolutional (PAC) codes, as a concatenated coding scheme based on polar codes, is able to approach the finite-length bound of binary-input AWGN channel at short blocklengths. In this paper, we extend PAC codes to the fields of source coding and joint source-channel coding and show that they can also approach the corresponding finite-length bounds at short blocklengths.

This is a chapter of the upcoming "A Concise Encyclopedia of Coding Theory", W.C. Huffman, J.-L. Kim, and P. Sole' Eds., CRC Press. The chapter gives an introduction to the mathematical theory of rank-metric codes. Treated topics include: definition of rank metric, equivalence of codes, support of a codeword and of a code, duality, weight enumerators and MacWilliams identities, higher rank weights, MRD codes, optimal anticodes, and q-polymatroids associated to a rank-metric code.