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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-10-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001182045</rptOwnerCik>
            <rptOwnerName>ALBAUGH JAMES F</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>27552 NORTH 103RD WAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SCOTTSDALE</rptOwnerCity>
            <rptOwnerState>AZ</rptOwnerState>
            <rptOwnerZipCode>85262</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Phantom Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2016-10-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>122.8</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>91.61</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>122.8</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>122.8</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Each phantom stock unit is the economic equivalent of one share of the Issuer's common stock.</footnote>
        <footnote id="F2">The phantom stock units were awarded on October 1, 2016 pursuant to an automatic quarterly grant under the Harris Corporation 2005 Directors' Deferred Compensation Plan.  The phantom stock units are to be settled in cash upon the reporting person's retirement or other events.  The reporting person may also transfer the phantom stock units into alternative investment accounts in certain other instances if applicable ownership guidelines are satisfied.</footnote>
    </footnotes>

    <remarks>Exhibit List:

Exhibit 24 - Power of Attorney</remarks>

    <ownerSignature>
        <signatureName>By:  /s/ Scott T. Mikuen, Attorney-in-Fact,
For:  James F. Albaugh</signatureName>
        <signatureDate>2016-10-04</signatureDate>
    </ownerSignature>
</ownershipDocument>
