<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-11-13</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0000202058</issuerCik><issuerName>HARRIS CORP /DE/</issuerName>        <issuerTradingSymbol>HRS</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001219116</rptOwnerCik><rptOwnerName>BALLANTYNE RICHARD 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>0</isDirector><isOfficer>1</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther><officerTitle>VP - General Counsel and Secy</officerTitle></reportingOwnerRelationship></reportingOwner><nonDerivativeTable><nonDerivativeTransaction><securityTitle><value>Common Stock, Par Value $1.00</value></securityTitle><transactionDate><value>2003-11-13</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>M</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>2755.0000</value><footnoteId id="F1" /></transactionShares><transactionPricePerShare><value>24.7278</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>33994.3700</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction><nonDerivativeTransaction><securityTitle><value>Common Stock, Par Value $1.00</value></securityTitle><transactionDate><value>2003-11-13</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>F</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>1797.0000</value><footnoteId id="F1" /></transactionShares><transactionPricePerShare><value>37.8900</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>32197.3700</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction><nonDerivativeTransaction><securityTitle><value>Common Stock, Par Value $1.00</value></securityTitle><transactionDate><value>2003-11-13</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>F</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>255.0000</value><footnoteId id="F1" /></transactionShares><transactionPricePerShare><value>37.8900</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>31942.3700</value><footnoteId id="F2" /></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction></nonDerivativeTable><derivativeTable><derivativeTransaction><securityTitle><value>Non-Qualified Stock Option (right to buy)</value></securityTitle><conversionOrExercisePrice><value>24.7278</value></conversionOrExercisePrice><transactionDate><value>2003-11-13</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>M</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>2755.0000</value></transactionShares><transactionPricePerShare><value>0</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><value>2002-08-27</value></exerciseDate><expirationDate><value>2009-08-27</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock, Par Value $1.00</value></underlyingSecurityTitle><underlyingSecurityShares><value>2755.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>0</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction><derivativeTransaction><securityTitle><value>Non-Qualified Stock Option (right to buy)</value></securityTitle><conversionOrExercisePrice><value>37.7500</value></conversionOrExercisePrice><transactionDate><value>2003-11-13</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>A</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>1797.0000</value></transactionShares><transactionPricePerShare><value>0</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><value>2004-05-13</value></exerciseDate><expirationDate><value>2009-08-27</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock, Par Value $1.00</value></underlyingSecurityTitle><underlyingSecurityShares><value>1797.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>1797.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction></derivativeTable><footnotes><footnote id="F1">Stock swap exercise (referenced in Table II) and disposition of shares upon tax withholding.</footnote><footnote id="F2">Aggregate of 31,942.37 shares listed in Column 5 of Table I includes 6,000 performance shares previously reported and subject to adjustment.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>/s/ Richard L. Ballantyne</signatureName><signatureDate>2003-11-14</signatureDate></ownerSignature></ownershipDocument>

