<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2004-01-02</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0000202058</issuerCik><issuerName>HARRIS CORP /DE/</issuerName>        <issuerTradingSymbol>HRS</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001220679</rptOwnerCik><rptOwnerName>LANCE HOWARD L</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>CORPORATE HEADQUARTERS</rptOwnerStreet1><rptOwnerStreet2>1025 W. NASA BOULEVARD</rptOwnerStreet2><rptOwnerCity>MELBOURNE</rptOwnerCity><rptOwnerState>FL</rptOwnerState><rptOwnerZipCode>32919</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>1</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther><officerTitle>Chairman, President, and CEO</officerTitle></reportingOwnerRelationship></reportingOwner><derivativeTable><derivativeTransaction><securityTitle><value>Phantom Stock Units</value></securityTitle><conversionOrExercisePrice><value>0</value><footnoteId id="F1" /></conversionOrExercisePrice><transactionDate><value>2004-01-02</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>I</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>77.8000</value></transactionShares><transactionPricePerShare><value>38.3100</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><footnoteId id="F2" /></exerciseDate><expirationDate><footnoteId id="F2" /></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock, Par Value $1.00</value></underlyingSecurityTitle><underlyingSecurityShares><value>77.8000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>352.8000</value><footnoteId id="F3" /></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction></derivativeTable><footnotes><footnote id="F1">Convertible on a 1-for-1 basis.</footnote><footnote id="F2">Reported phantom stock units acquired (in an exempt transaction) under Harris Corporation's Supplemental Executive Retirement Plan and will be settled in cash following the reporting person's retirement, termination of service, or other specified events.</footnote><footnote id="F3">The aggregate of 352.80 phantom stock units includes .75 stock unit acquired through dividend reinvestment in Harris Corporation's Supplemental Executive Retirement Plan on 11/19/03.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>/s/ Howard L. Lance</signatureName><signatureDate>2004-01-06</signatureDate></ownerSignature></ownershipDocument>

