Problem
Research questions and friction points this paper is trying to address.
function-correcting codes
systematic encodings
redundancy cost
linear functions
relative generalized Hamming weight
On systematicity of linear function-correcting codes
🤖 AI Summary
研究线性函数纠错码的系统性约束下的冗余成本，引入函数分离距离，并解决自由和系统的线性分离问题。
📝 Abstract
The standard formulation of function-correcting codes uses systematic encodings. We study the redundancy cost of this constraint when both the prescribed function and the encoding are linear. We introduce the function-separation distance and show that several classical unequal error protection parameters are special cases. For linear functions and encodings, this distance is the first relative generalized Hamming weight of the code relative to the encoded kernel. We formulate free and systematic linear separation problems. We prove that the optimal free redundancy depends only on the rank of the function, and determine the optimal systematic redundancy for prescribed separations $d\leq3$.
Innovation
Methods, ideas, or system contributions that make the work stand out.
function-separation distance
linear function-correcting codes
relative generalized Hamming weight
systematic redundancy
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