Etymology

The case for ON input depends on how the absence of palatalization of /k/ is explained. PGmc *rauk- (ablaut variant derived from *reukan- 'to smoke') has reflexes OIcel reykr 'smoke, steam', OE rēc 'smoke', OFris rēk, (a-stem) OS rōk, OHG rouh. The palatalization caused by the i-mutation of the stem in OE is reflected in ME spellings in <ch>. OED3 very reasonably suggests a combination of factors is behind variants indicating instead /k/: (1) analogical levelling from elsewhere in the paradigm before a back vowel; (2) the influence of Scandinavian cognates; (3) influence from the corresponding v. OE rēocan.

PGmc Ancestor

*raukiz

Proposed ON Etymon (OIcel representative)

reykr 'smoke, steam'
(ONP reykr (sb.))

Other Scandinavian Reflexes

Far reykur, Icel reykur, Norw røyk, Dan røg, Sw rök

OE Cognate

rēc 'smoke'

Phonological and morphological markers

[absence of palatalization of */k/] (possibly diagnostic)

Summary category

CC2c

Attestation

Spellings indicating /k/ are attested from the 13c. onwards; MED's citations are predominantly from N texts (but there is no evident dial bias in the distribution of palatalized forms, which also occur in e.g. WA  and SJ).

Occurrences in the Gersum Corpus

WA 1566

Bibliography

MED rẹ̄k(e (n.3) , OED3 (n.1) , HTOED , EDD reek (sb.1 and v.1), de Vries reykr, Mag. reykur, Orel *raukiz, Kroonen rauki-