Definition of "linnen"

Great, good company at dinner, among others Sir Martin Noell, who told us the dispute between him, as farmer of the Additional Duty, and the East India Company, whether callicos be linnen or no; which he says it is, having been ever esteemed so: they say it is made of cotton woole, and grows upon trees, not like flax or hempe.

1663 March 9 (date written; Gregorian calendar), Samuel Pepys, Mynors Bright, transcriber, “February 27th, 1662–1663”, in Henry B[enjamin] Wheatley, editor, The Diary of Samuel Pepys […], volume IV, London: George Bell & Sons […]; Cambridge: Deighton Bell & Co., published 1894, pages 57–58