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===Extensions by Taylor, Lempel, and Golomb===
Generation of new Costas arrays by adding or subtracting a row/column or two with a 1 or a pair of 1's in a corner were published in a paper focused on generation methods<ref>Solomon Golomb, ''Algebraic constructions for Costas arrays'', J. Comb. Theory Series A, volume 7 (1984), pp 1143–1163</ref> and in Golomb and Taylor's landmark 1984 paper.{{sfnp|Golomb|Taylor|1984}}
More sophisticated methods of generating new Costas arrays by deleting rows and columns of existing Costas arrays that were generated by the Welch, Lempel or Golomb generators were published in 1992.<ref>Solomon W. Golomb, ''The T_4and G_4 Constructions for Costas Arrays'', IEEE Transactions on Information Theory, volume 38 (1992), pp 1404–1406.</ref> There is no upper limit on the order for which these generators will produce Costas arrays.
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