\documentclass[11pt]{article} \usepackage{amsmath, amssymb, amsthm, graphicx, hyperref, url, booktabs, multirow, caption, subcaption, geometry, setspace, algorithm, algorithmic, enumitem, mathtools, tikz} \usepackage{cleveref} \geometry{margin=1in} \setstretch{1.1} \theoremstyle{definition} \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{corollary}[theorem]{Corollary} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{definition}[theorem]{Definition} \newtheorem{remark}[theorem]{Remark} \newtheorem{example}[theorem]{Example} \newcommand{\CC}{\mathbb{C}} \newcommand{\RR}{\mathbb{R}} \newcommand{\ZZ}{\mathbb{Z}} \newcommand{\FF}{\mathbb{F}} \newcommand{\Tr}{\mathrm{Tr}} \newcommand{\diag}{\mathrm{diag}} \newcommand{\supp}{\mathrm{supp}} \newcommand{\diam}{\mathrm{diam}} \newcommand{\norm}[1]{\|#1\|} \newcommand{\opnorm}[1]{\|#1\|_{\infty}} \newcommand{\trnorm}[1]{\|#1\|_{1}} \newcommand{\frob}[1]{\|#1\|_{F}} \newcommand{\inner}[2]{\langle #1, 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\newcommand{\codeparamUUUUUUUUUUUUUU}{[\![n,k,d]\!]} \newcommand{\codeparamVVVVVVVVVVVVVV}{[\![n,k,d]\!]} \newcommand{\codeparamWWWWWWWWWWWWWW}{[\![n,k,d]\!]} \newcommand{\codeparamXXXXXXXXXXXXXX}{[\![n,k,d]\!]} \newcommand{\codeparamYYYYYYYYYYYYYY}{[\![n,k,d]\!]} \newcommand{\codeparamZZZZZZZZZZZZZZ}{[\![n,k,d]\!]} \newcommand{\codeparamAAAAAAAAAAAAAAA}{[\![n,k,d]\!]} \newcommand{\codeparamBBBBBBBBBBBBBBB}{[\![n,k,d]\!]} \newcommand{\codeparamCCCCCCCCCCCCCCCC}{[\![n,k,d]\!]} \newcommand{\codeparamDDDDDDDDDDDDDDDD}{[\![n,k,d]\!]} \newcommand{\codeparamEEEEEEEEEEEEEEEE}{[\![n,k,d]\!]} \newcommand{\codeparamFFFFFFFFFFF}{[\![n,k,d]\!]} \newcommand{\codeparamGGGGGGGGGGGGGGG}{[\![n,k,d]\!]} \newcommand{\codeparamHHHHHHHHHHHHHHH}{[\![n,k,d]\!]} \newcommand{\codeparamIIIIIIIIIIIIIII}{[\![n,k,d]\!]} \newcommand{\codeparamJJJJJJJJJJJJJJJ}{[\![n,k,d]\!]} \newcommand{\codeparamKKKKKKKKKKKKKKK}{[\![n,k,d]\!]} \newcommand{\codeparamLLLLLLLLLLLLLLL}{[\![n,k,d]\!]} \newcommand{\codeparamMMMMMMMMMMMMMMM}{[\![n,k,d]\!]} \newcommand{\codeparamNNNNNNNNNNNNNNN}{[\![n,k,d]\!]} \newcommand{\codeparamOOOOOOOOOOOOOOO}{[\![n,k,d]\!]} \newcommand{\codeparamPPPPPPPPPPPPPPP}{[\![n,k,d]\!]} \newcommand{\codeparamQQQQQQQQQQQQQQQ}{[\![n,k,d]\!]} \newcommand{\codeparamRRRRRRRRRRRRRRR}{[\![n,k,d]\!]} \newcommand{\codeparamSSSSSSSSSSSSSSS}{[\![n,k,d]\!]} \newcommand{\codeparamTTTTTTTTTTTTTTT}{[\![n,k,d]\!]} \newcommand{\codeparamUUUUUUUUUUUUUUU}{[\![n,k,d]\!]} \newcommand{\codeparamVVVVVVVVVVVVVVV}{[\![n,k,d]\!]} \newcommand{\codeparamWWWWWWWWWWWWWWW}{[\![n,k,d]\!]} \newcommand{\codeparamXXXXXXXXXXXXXXX}{[\![n,k,d]\!]} \newcommand{\codeparamYYYYYYYYYYYYYYY}{[\![n,k,d]\!]} \newcommand{\codeparamZZZZZZZZZZZZZZZ}{[\![n,k,d]\!]} \newcommand{\codeparamAAAAAAAAAAAAAAAA}{[\![n,k,d]\!]} \newcommand{\codeparamBBBBBBBBBBBBBBBB}{[\![n,k,d]\!]} \newcommand{\codeparamCCCCCCCCCCCCCCCCC}{[\![n,k,d]\!]} \newcommand{\codeparamDDDDDDDDDDDDDDDDD}{[\![n,k,d]\!]} \newcommand{\codeparamEEEEEEEEEEEEEEEEE}{[\![n,k,d]\!]} \newcommand{\codeparamFFFFFFFFFFF}{[\![n,k,d]\!]} \newcommand{\codeparamGGGGGGGGGGGGGGGG}{[\![n,k,d]\!]} \newcommand{\codeparamHHHHHHHHHHHHHHHH}{[\![n,k,d]\!]} \newcommand{\codeparamIIIIIIIIIIIIIIII}{[\![n,k,d]\!]} \newcommand{\codeparamJJJJJJJJJJJJJJJJ}{[\![n,k,d]\!]} \newcommand{\codeparamKKKKKKKKKKKKKKKK}{[\![n,k,d]\!]} \newcommand{\codeparamLLLLLLLLLLLLLLLL}{[\![n,k,d]\!]} \newcommand{\codeparamMMMMMMMMMMMM