<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2005-04-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000202058</issuerCik>
        <issuerName>HARRIS CORP /DE/</issuerName>
        <issuerTradingSymbol>HRS</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001220676</rptOwnerCik>
            <rptOwnerName>HELDRETH NICK E</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 - Human Resources</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Phantom Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2005-04-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>I</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>9.89</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>32.56</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>9.89</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4309.25</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">On March 30, 2005, Harris Corporation distributed a stock dividend, payable to all holders of record of common stock on March 14, 2005, of 1 share of common stock for each share of common stock outstanding.  The aggregate of 4,309.25 phantom stock units includes phantom units acquired on 3/30/05 as a result of the 2-for-1 split and 3.82 units acquired through dividend reinvestment in Harris Corporation's Supplemental Executive Retirement Plan on 3/10/05.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Nick E. Heldreth</signatureName>
        <signatureDate>2005-04-05</signatureDate>
    </ownerSignature>
</ownershipDocument>
